System and method for controlling gain and timing phase in a presence of a first least mean square filter using a second adaptive filter

ABSTRACT

A system for controlling gain and timing phase includes a variable gain amplifier (VGA) responsive to an input signal, and an analog-to-digital converter (ADC) responsive to a VGA output. A first filter, with tap weight coefficients updated by a first least mean square (LMS) engine, is responsive to an ADC output. At least one tap weight coefficient of the first filter is constrained. A second filter, with tap weight coefficients updated by an adaptation engine, is responsive to a first filter output. The complexity of the second filter is less than or equal to the complexity of the first filter. The system includes: a timing phase controller, in communication with the ADC and responsive to a second filter output, for controlling ADC timing phase; and/or a gain controller, in communication with the VGA and responsive to the second filter output, for controlling VGA gain.

This application claims priority under 35 U.S.C. § 119(e) to U.S.Provisional Application No. 60/457,717, filed on Mar. 25, 2003, theentire content of which is hereby incorporated herein by reference.

BACKGROUND

1. Field of the Invention

The present invention relates to Least Mean Square (LMS) filters. Moreparticularly, the present invention relates to a system and method forcontrolling gain and timing phase in the presence of a first LMS filterusing a second adaptive filter.

2. Background Information

The Least Mean Square (LMS) adaptation algorithm is known to providegood error rate performance for sequence detectors in applications suchas, for example, digital data detectors (e.g., read channel devices formagnetic recording), data communication and the like. The LMS algorithmis updated according to Equation (1):C _(N)(n+1)=C _(N)(n)+μ*E(n)*X _(N)(n)  (1)According to Equation (1), C_(N)(n+1) is a vector of N tap weightcoefficients of a filter for the next iteration (i.e., the next timesampling interval of the input signal), i.e., C_(N)(n+1)=[C₀(n+1),C(n+1), . . . , C_(N−1)(n+1)]. The filter can be, for example, a FiniteImpulse Response (FIR) filter or an Infinite Impulse Response filter. AFIR filter produces an output that is a weighted sum of the current andpast inputs to the filter. An IIR filter produces an output that is aweighted sum of the current and past inputs to the filter and pastoutputs of the filter. In Equation (1), C_(N)(n) is a vector of N tapweight coefficients of the filter for the current iteration (i.e., thecurrent sampling interval of the input signal), i.e., C_(N)(n)=[C₀(n),C₁(n), . . . , C_(N−1)(n)]. The gain constant or step-size parameter μis a scalar value that generally controls the rate at which the LMSalgorithm converges, with its value generally being between, forexample, zero and one. E(n) is a scalar value representing the errorbetween the value of the signal input to the filter and the idealnoiseless value of that input signal. For data communication, an outputof the filter can be in communication with an input of a sequencedetector, and an output of the sequence detector can be in communicationwith an input of a reconstruction filter, a target channel responsefilter, or the like. The ideal noiseless value can be estimated byconvolving the output of the sequence detector with the target channelresponse. In Equation (1), X_(N)(n) is a vector of N delayed inputsamples to the filter, i.e., X_(N)(n)=[X(k), X(k−1), . . . ,X(k−(N−1))].

In data communication receivers with gain recovery and/or timing phaserecovery, it is generally necessary to constrain the LMS algorithm tominimize the interaction between the LMS adaptation and the gain andtiming phase recovery. For example, for a filter having tap weightcoefficients updated according to the LMS algorithm, at least two of themain tap weight coefficients of the filter can be constrained and notadapted. A Zero-Forcing (ZF) Automatic Gain Control (AGC) algorithm canbe used to control the gain of the system. In such a configuration,there can be an undesirable interaction between the filter having tapweight coefficients updated according to the LMS algorithm and the ZFAGC. In the presence of signal noise, minimization of the Mean SquareError (MSE) by the LMS algorithm on the input signal through the filtercan require that the gain of the system be slightly lowered relative tothe noiseless case. However, the ZF AGC algorithm generally does notmake adjustments to the overall gain setting, even in the presence ofnoise. With the ZF AGC algorithm maintaining a higher gain than desiredby the filter having tap weight coefficients updated according to theLMS algorithm, the resultant higher-gain situation can cause theconstrained LMS algorithm to converge to a sub-optimal state that can befar from the optimal error rate performance of the data receiver.

In addition, there can be another bias (or biases) in the timing phaserecovery of the data receiver. This can be caused by, for example,implementation inaccuracy (e.g., quantization effects), data patterndependencies (e.g., highly asymmetric waveforms), and the like. Theconstrained LMS algorithm generally cannot correct for the biascondition properly, because two or more of the main tap weightcoefficients of the filter are not allowed to adapt. Consequently, thetap weight coefficients that are allowed to adapt can over-correct,which can result in the tap weight coefficients of the filter convergingto a state that also yields sub-optimal error rate performance.

SUMMARY OF THE INVENTION

A method and system are disclosed for a system and method forcontrolling gain and timing phase in the presence of a first Least MeanSquare (LMS) filter using a second adaptive filter. In accordance withexemplary embodiments, according to a first aspect of the presentinvention, an information communication system can include a variablegain amplifier (VGA). The VGA can be responsive to an input signal ofthe information communication system. The information communicationsystem can include an analog-to-digital converter (ADC). The ADC can beresponsive to an output of the VGA. The information communication systemcan include a first filter. Tap weight coefficients of the first filtercan be updated according to a first least mean square (LMS) engine. Thefirst filter can be responsive to an output of the ADC. At least one tapweight coefficient of the first filter can be constrained. Theinformation communication system can include a second filter. Tap weightcoefficients of the second filter can be updated according to anadaptation engine. The adaptation engine can comprise a second LMSengine or a zero-forcing engine. The second filter can be responsive toan output of the first filter. The number of tap weight coefficients ofthe second filter can be less than or equal to the number of the tapweight coefficients of the first filter. The information communicationsystem can include either or both of a gain controller for controllinggain of the VGA, wherein the gain controller can in communication withthe VGA and responsive to the output of the second filter, and a timingphase controller for controlling timing phase of the ADC, wherein thetiming phase controller can be in communication with the ADC andresponsive to an output of the second filter.

According to an exemplary embodiment of the first aspect, at least twotap weight coefficients of the first filter can be constrained. A valueof at least one tap weight coefficient of the second filter can beupdated to provide a gain of the second filter that is associated with achange in gain error from the first filter. The gain of the secondfilter can be configured to cause the gain controller to modify a gainof the VGA to compensate for the change in gain error from the firstfilter. Additionally or alternatively, a value of at least one tapweight coefficient of the second filter can be updated to provide atiming phase of the second filter that is associated with a change intiming phase error introduced by the first filter. The timing phase ofthe second filter can be configured to cause the timing phase controllerto modify a timing phase of the ADC to compensate for the change intiming phase error introduced by the first filter.

According to the first aspect, the second filter can comprise either atwo-tap filter or a three-tap filter. For example, the tap weightcoefficients of the two-tap filter can comprise “a” and “1+b”,respectively, and the tap weight coefficients of the three-tap filtercan comprise “a”, “1+b”, and “−a”, respectively. The tap weightcoefficient “a” can be updated according to the equation:a[n+1]=a[n]−α*Δθ,wherein a[n+1] comprises the value of the tap weight coefficient “a” forthe next sampling time of the input signal, a[n] comprises the value ofthe tap weight coefficient “a” for the current sampling time of theinput signal, α comprises a first gain constant, and Δθ comprises thechange in timing phase error associated with the first filter.

According to an exemplary embodiment of the first aspect, the firstfilter can comprise N tap weight coefficients, wherein N comprises atleast four. For purposes of illustration and not limitation, a third tapweight coefficient C₃ and a fourth tap weight coefficient C₄ of thefirst filter can be constrained. Thus, Δθ can be updated according tothe equation:

${{\Delta\theta} = \frac{\left( {{{- \Delta}\; C_{3}*K_{e}} - {\Delta\; C_{4}*K_{o}}} \right)}{K_{e}^{2} + K_{o}^{2}}},$wherein ΔC₃ and ΔC₄ are updated according to the equations:ΔC ₃ =μ*E[n]*X[n−3] andΔC ₄ =μ*E[n]*X[n−4], respectively,wherein μ comprises a second gain constant, E[n] comprises an errorsignal for the current sampling time of the input signal, X[n−3]comprises the value of the input signal at the third previous samplingtime of the input signal, and X[n−4] comprises the value of the inputsignal at the fourth previous sampling time of the input signal.According to the first aspect, K_(e) and K_(o) can be updated accordingto the equations:

${{K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},}\mspace{20mu}$and

${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$respectively,wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1”otherwise, M can be determined according to the equation:M=TRUNCATE((N−1)/2), andP can be determined according to the equation:P=TRUNCATE(((N−1)/2)−0.5).According to an alternative exemplary embodiment of the first aspect,K_(e) and K_(o) can each comprise a predetermined value. The errorsignal E[n] can comprise the difference between an output of the firstfilter and the output of a reconstruction filter. The reconstructionfilter can be responsive to an output of a sequence detector. Thesequence detector can be responsive to an output of the first filter.

According to an alternative exemplary embodiment of the first aspect,the first filter can comprise N tap weight coefficients, wherein Ncomprises at least four. For purposes of illustration and notlimitation, a third tap weight coefficient C₃ and a fourth tap weightcoefficient C₄ of the first filter can be constrained. Thus, Δθ can beupdated according to the equation:Δθ=(−ΔC ₃ *K _(e) −ΔC ₄ *K _(o)),wherein ΔC₃ and ΔC₄ are updated according to the equations:ΔC ₃ =μ*E[n]*X[n−3] andΔC ₄ =μ*E[n]*X[n−4], respectively,wherein μ comprises a second gain constant, E[n] comprises an errorsignal for the current sampling time of the input signal, X[n−3]comprises the value of the input signal at the third previous samplingtime of the input signal, and X[n−4] comprises the value of the inputsignal at the fourth previous sampling time of the input signal.According to the first aspect, K_(e) and K_(o) can be updated accordingto the equations:

${{K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},}\mspace{20mu}$and

${{K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},}\;$respectively,wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1”otherwise, M can be determined according to the equation:M=TRUNCATE((N−1)/2), andP can be determined according to the equation:P=TRUNCATE(((N−1)/2)−0.5).According to an alternative exemplary embodiment of the first aspect,K_(e) and K_(o) can each comprise a predetermined value.

According to the first aspect, the information communication system caninclude a sequence detector. The sequence detector can be responsive toan output of the first filter. The information communication system caninclude a reconstruction filter. The reconstruction filter can beresponsive to an output of the sequence detector. The informationcommunication system can also include an error generator. The errorgenerator can be responsive to the output of the first filter and anoutput of the reconstruction filter. The error generator can generatethe error signal E[n] comprising a difference between the output of thefirst filter and the output of the reconstruction filter.

According to the first aspect, the tap weight coefficient “b” can beupdated according to the equation:b[n+1]=b[n]−β*ΔΓ,wherein b[n+1] comprises the value of the tap weight coefficient “b” forthe next sampling time of the input signal, b[n] comprises the value ofthe tap weight coefficient “b” for the current sampling time of theinput signal, β comprises a first gain constant, and ΔΓ comprises thechange in gain error from the first filter. According to an exemplaryembodiment of the first aspect, the first filter can comprise N tapweight coefficients, wherein N comprises at least four. For purposes ofillustration and not limitation, a third tap weight coefficient C₃ and afourth tap weight coefficient C₄ of the first filter can be constrained.Thus, ΔΓ can be updated according to equation:

${{\Delta\Gamma} = \frac{\left( {{{- \Delta}\; C_{3}*K_{o}} + {\Delta\; C_{4}*K_{e}}} \right)}{\sqrt{K_{e}^{2} + K_{o}^{2}}}},$wherein ΔC₃ and ΔC₄ are updated according to the equations:ΔC ₃ =μ*E[n]*X[n−3] andΔC ₄ =μ*E[n]*X[n−4], respectively,wherein μ comprises a second gain constant, E[n] comprises an errorsignal for the current sampling time of the input signal, X[n−3]comprises the value of the input signal at the third previous samplingtime of the input signal, and X[n−4] comprises the value of the inputsignal at the fourth previous sampling time of the input signal.According to the first aspect, K_(e) and K_(o) can be updated accordingto the equations:

${{K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},}\mspace{14mu}$and

$\;{{K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},}\;$respectively,wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1”otherwise, M can be determined according to the equation:M=TRUNCATE((N−1)/2), andP can be determined according to the equation:P=TRUNCATE(((N−1)/2)−0.5).According to an alternative exemplary embodiment of the first aspect,K_(e) and K_(o) can each comprise a predetermined value. The errorsignal E[n] can comprise the difference between the output of the firstfilter and the output of the reconstruction filter.

According to an alternative exemplary embodiment of the first aspect,the first filter can comprise N tap weight coefficients, wherein Ncomprises at least four. For purposes of illustration and notlimitation, a third tap weight coefficient C₃ and a fourth tap weightcoefficient C₄ of the first filter can be constrained. Thus, ΔΓ can beupdated according to the equation:ΔΓ=(−ΔC ₃ *K _(o) +ΔC ₄ *K _(e)),wherein ΔC₃ and ΔC₄ are updated according to the equations:ΔC ₃ =μ*E[n]*X[n−3] andΔC ₄ =μ*E[n]*X[n−4], respectively,wherein μ comprises a second gain constant, E[n] comprises an errorsignal for the current sampling time of the input signal, X[n−3]comprises the value of the input signal at the third previous samplingtime of the input signal, and X[n−4] comprises the value of the inputsignal at the fourth previous sampling time of the input signal.According to the first aspect, K_(e) and K_(o) can be updated accordingto the equations:

${{K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},}\mspace{20mu}$and

${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$respectively,wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1”otherwise, M can be determined according to the equation:M=TRUNCATE((N−1)/2), andP can be determined according to the equation:P=TRUNCATE(((N−1)/2)−0.5).According to an alternative exemplary embodiment of the first aspect,K_(e) and K_(o) can each comprise a predetermined value. The errorsignal E[n] can comprise the difference between the output of the firstfilter and the output of the reconstruction filter.

According to the first aspect, the information communication system caninclude an error generator responsive to an output of the reconstructionfilter. The error generator can be in communication between an output ofthe second filter and inputs of the timing phase controller and the gaincontroller. According to an alternative exemplary embodiment of thefirst aspect, the timing phase controller can comprise the errorgenerator. The timing phase controller can be responsive to the outputof the reconstruction filter. According to the alternative exemplaryembodiment, the gain controller can comprise the error generator. Thegain controller can be responsive to the output of the reconstructionfilter. The first filter and the second filter can each comprise aFinite Impulse Response filter. According to an exemplary embodiment ofthe first aspect, a disk drive can comprise the informationcommunication system. At least the VGA, ADC, first filter, secondfilter, and at least one of the timing phase controller and gaincontroller can be formed on a monolithic substrate. The informationcommunication system can be compliant with a standard selected from thegroup consisting of 802.11, 802.11a, 802.11b, 802.11g and 802.11i.

According to a second aspect of the present invention, a method forcontrolling at least one of gain and timing phase can comprise the stepsof: a.) amplifying an input signal to generate an amplified signal; b.)converting the amplified signal into a digital signal to generate aconverted signal; c.) filtering the converted signal to generate a firstfiltered signal in accordance with a first plurality of filtercoefficients, wherein the first plurality of filter coefficients areupdated according to a first LMS process, and wherein at least onefilter coefficient of the first plurality of filter coefficients isconstrained; d.) filtering the first filtered signal to generate asecond filtered signal in accordance with a second plurality of filtercoefficients, wherein the second plurality of filter coefficients of thesecond filter are updated according to an adaptation process, andwherein a number of filter coefficients of the second plurality offilter coefficients comprises one of less than and equal to a number ofthe filter coefficients of the first plurality of filter coefficients;e.) controlling a gain of step (a.) in response to the second filteredsignal; and f.) controlling a timing phase of step (b.) in response tothe second filtered signal. The adaptation process used to update thesecond plurality of filter coefficients can comprise a second LMSprocess or a zero-forcing process.

According to an exemplary embodiment of the second aspect, at least twofilter coefficients of the first plurality of filter coefficients can beconstrained. The method can include the steps of: g.) updating a valueof at least one filter coefficient of the second plurality of filtercoefficients to provide a gain of step (d.) that is associated with achange in gain error from step (c.); and h.) modifying the gain of step(a.) based upon the gain of step (d.), to compensate for the change ingain error from step (c.). Additionally or alternatively, the method caninclude the steps of: g.) updating a value of at least one filtercoefficient of the second plurality of filter coefficients to provide atiming phase of step (d.) that is associated with a change in timingphase error introduced by step (c.); and h.) modifying a timing phase ofstep (b.) based upon the timing phase of step (d.), to compensate forthe change in timing phase error introduced by step (c.).

According to an exemplary embodiment of the second aspect, the secondplurality of filter coefficients can comprise two or three filtercoefficients. The two filter coefficients of the second plurality offilter coefficients can comprise “a” and “1+b”, respectively, and thethree filter coefficients of the second plurality of filter coefficientscan comprise “a”, “1+b”, and “−a”, respectively. The method can includethe step of: g.) updating the filter coefficient “a” according to theequation:a[n+1]=a[n]−α*Δθ,wherein a[n+1] comprises the value of the tap weight coefficient “a” forthe next sampling time of the input signal, a[n] comprises the value ofthe tap weight coefficient “a” for the current sampling time of theinput signal, α comprises a first gain constant, and Δθ comprises thechange in timing phase error associated with step (c.).

According to an exemplary embodiment of the second aspect, the firstplurality of filter coefficients can comprise N filter coefficients,wherein N comprises at least four. For purposes of illustration and notlimitation, a third filter coefficient C₃ and a fourth filtercoefficient C₄ of the first plurality of filter coefficients can beconstrained. The method can comprise the steps of: h.) updating Δθaccording to the equation:

${{\Delta\;\theta} = \frac{\left( {{{- \Delta}\; C_{3}*K_{e}} - {\Delta\; C_{4}*K_{o}}} \right)}{K_{e}^{2} + K_{o}^{2}}},$wherein ΔC₃ and ΔC₄ are updated according to the equations:ΔC ₃ =μ*E[n]*X[n−3] andΔC ₄ =μ*E[n]*X[n−4], respectively,wherein μ comprises a second gain constant, E[n] comprises an errorsignal for the current sampling time of the input signal, X[n−3]comprises the value of the input signal at the third previous samplingtime of the input signal, and X[n−4] comprises the value of the inputsignal at the fourth previous sampling time of the input signal; and i.)updating K_(e) and K_(o) according to the equations:

${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$and

${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$respectively,wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1”otherwise, M can be determined according to the equation:M=TRUNCATE((N−1)/2), andP can be determined according to the equation:P=TRUNCATE(((N−1)/2)−0.5).According to an alternative exemplary embodiment of the second aspect,K_(e) and K_(o) can each comprise a predetermined value. The method canfurther comprise the steps of: i.) detecting an information sequence inthe first filtered signal; j.) reconstructing an information signal fromthe detected information sequence; and k.) generating the error signalE[n] comprising a difference between the first filtered signal and thereconstructed information signal.

According to an alternative exemplary embodiment of the second aspect,the first plurality of filter coefficients can comprise N filtercoefficients, wherein N comprises at least four. For purposes ofillustration and not limitation, a third filter coefficient C₃ and afourth filter coefficient C₄ of the first plurality of filtercoefficients can be constrained. The method can include the steps of:h.) updating Δθ according to the equation:Δθ=(−ΔC ₃ *K _(e) −ΔC ₄ *K _(o)),wherein ΔC₃ and ΔC₄ are updated according to the equations:ΔC ₃ =μ*E[n]*X[n−3] andΔC ₄ =μ*E[n]*X[n−4], respectively,wherein μ comprises a second gain constant, E[n] comprises an errorsignal for the current sampling time of the input signal, X[n−3]comprises the value of the input signal at the third previous samplingtime of the input signal, and X[n−4] comprises the value of the inputsignal at the fourth previous sampling time of the input signal; and i.)updating K_(e) and K_(o) according to the equations:

${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$and

${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$respectively,wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1”otherwise, M can be determined according to the equation:M=TRUNCATE((N−1)/2), andP can be determined according to the equation:P=TRUNCATE(((N−1)/2)−0.5).According to an alternative exemplary embodiment of the second aspect,K_(e) and K_(o) can each comprise a predetermined value. The method canfurther comprise the steps of: i.) detecting an information sequence inthe first filtered signal; j.) reconstructing an information signal fromthe detected information sequence; and k.) generating the error signalE[n] comprising a difference between the first filtered signal and thereconstructed information signal.

According to the second aspect, the method can include the step of: g.)updating the tap weight coefficient “b” according to the equation:b[n+1]=b[n]−β*ΔΓ,wherein b[n+1] comprises the value of the tap weight coefficient “b” forthe next sampling time of the input signal, b[n] comprises the value ofthe tap weight coefficient “b” for the current sampling time of theinput signal, β comprises a first gain constant, and ΔΓ comprises thechange in gain error from step (c.). According to an exemplaryembodiment of the second aspect, the first plurality of filtercoefficients can comprise N filter coefficients, wherein N comprises atleast four. For purposes of illustration and not limitation, a thirdfilter coefficient C₃ and a fourth filter coefficient C₄ of the firstplurality of filter coefficients can be constrained. The method caninclude the steps of: h.) updating ΔΓ according to equation:

${{\Delta\;\Gamma} = \frac{\left( {{{- \Delta}\; C_{3}*K_{o}} + {\Delta\; C_{4}*K_{e}}} \right)}{\sqrt{K_{e}^{2} + K_{o}^{2}}}},$wherein ΔC₃ and ΔC₄ are updated according to the equations:ΔC ₃ =μ*E[n]*X[n−3] andΔC ₄ =μ*E[n]*X[n−4], respectively,wherein μ comprises a second gain constant, E[n] comprises an errorsignal for the current sampling time of the input signal, X[n−3]comprises the value of the input signal at the third previous samplingtime of the input signal, and X[n−4] comprises the value of the inputsignal at the fourth previous sampling time of the input signal; and i.)updating K_(e) and K_(o) according to the equations:

${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$and

${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$respectively,wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1”otherwise, M can be determined according to the equation:M=TRUNCATE((N−1)/2), andP can be determined according to the equation:P=TRUNCATE(((N−1)/2)−0.5).According to an alternative exemplary embodiment of the second aspect,K_(e) and K_(o) can each comprise a predetermined value. The method canfurther comprise the steps of: i.) detecting an information sequence inthe first filtered signal; j.) reconstructing an information signal fromthe detected information sequence; and k.) generating the error signalE[n] comprising a difference between the first filtered signal and thereconstructed information signal.

According to an alternative exemplary embodiment of the second aspect,the first plurality of filter coefficients can comprise N filtercoefficients, wherein N comprises at least four. For purposes ofillustration and not limitation, a third filter coefficient C₃ and afourth filter coefficient C₄ of the first plurality of filtercoefficients can be constrained. The method can comprise the steps of:h.) updating ΔΓ according to the equation:ΔΓ=(−ΔC ₃ *K _(o) +ΔC ₄ *K _(e)),wherein ΔC₃ and ΔC₄ are updated according to the equations:ΔC ₃ =μ*E[n]*X[n−3] andΔC ₄ =μ*E[n]*X[n−4], respectively,wherein μ comprises a second gain constant, E[n] comprises an errorsignal for the current sampling time of the input signal, X[n−3]comprises the value of the input signal at the third previous samplingtime of the input signal, and X[n−4] comprises the value of the inputsignal at the fourth previous sampling time of the input signal; and i.)updating K_(e) and K_(o) according to the equations:

${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$and

${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$respectively,wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1”otherwise, M can be determined according to the equation:M=TRUNCATE((N−1)/2), andP can be determined according to the equation:P=TRUNCATE(((N−1)/2)−0.5).According to an alternative exemplary embodiment of the second aspect,K_(e) and K_(o) can each comprise a predetermined value. The method canfurther comprise the steps of: i.) detecting an information sequence inthe first filtered signal; j.) reconstructing an information signal fromthe detected information sequence; and k.) generating the error signalE[n] comprising a difference between the first filtered signal and thereconstructed information signal.

According to the second aspect, the method can include the steps of: g.)detecting an information sequence in the first filtered signal; h.)reconstructing an information signal from the detected informationsequence; and i.) generating an error signal, wherein the error signalis associated with the reconstructed information signal. The method canbe compliant with a standard selected from the group consisting of802.11, 802.11a, 802.11b, 802.11g and 802.11i.

According to a third aspect of the present invention, an informationcommunication system can include means for amplifying an input signalreceived by the information communication system to generate anamplified signal. The information communication system can include meansfor converting the amplified signal into a digital signal to generate aconverted signal. The information communication system can include firstmeans for filtering the converted signal to generate a first filteredsignal. Tap weight coefficients of the first means for filtering can beupdated according to a first LMS adaptation means. At least one tapweight coefficient of the first means for filtering is constrained. Theinformation communication system can include second means for filteringthe first filtered signal to generate a second filtered signal. Tapweight coefficients of the second means for filtering can be updatedaccording to an adaptation means. The adaptation means can comprise asecond LMS adaptation means or a zero-forcing adaptation means. Thenumber of tap weight coefficients of the second means for filtering canbe less than or equal to the number of the tap weight coefficients ofthe first means for filtering. The information communication system caninclude either or both of means for controlling a gain of the means foramplifying in response to the second filtered signal and means forcontrolling a timing phase of the means for converting in response tothe second filtered signal.

According to an exemplary embodiment of the third aspect, at least twotap weight coefficients of the first means for filtering can beconstrained. The information communication system can include means forupdating a value of at least one tap weight coefficient of the secondmeans for filtering to provide a gain of the second means for filteringthat is associated with a change in gain error from the first means forfiltering. The information communication system can include means formodifying a gain of the means for amplifying based upon the gain of thesecond means for filtering, to compensate for the change in gain errorfrom the first means for filtering means. Additionally or alternatively,the information communication system can include means for updating avalue of at least one tap weight coefficient of the second means forfiltering to provide a timing phase of the second means for filteringthat is associated with a change in timing phase error introduced by thefirst means for filtering, and means for modifying a timing phase of themeans for converting based upon the timing phase of the second means forfiltering, to compensate for the change in timing phase error introducedby the first means for filtering.

According to an exemplary embodiment of the third aspect, the secondmeans for filtering can comprise either a two-tap filter means or athree-tap filter means. The tap weight coefficients of the two-tapfilter means can comprise “a” and “1+b”, respectively, and the tapweight coefficients of the three-tap filter means can comprise “a”,“1+b”, and “−a”, respectively. The information communication system caninclude means for updating the tap weight coefficient “a” according tothe equation:a[n+1]=a[n]−α*Δθ,wherein a[n+1] comprises the value of the tap weight coefficient “a” forthe next sampling time of the input signal, a[n] comprises the value ofthe tap weight coefficient “a” for the current sampling time of theinput signal, α comprises a first gain constant, and Δθ comprises thechange in timing phase error associated with the first means forfiltering.

According to an exemplary embodiment of the third aspect, the firstmeans for filtering can comprise N tap weight coefficients, wherein Ncomprises at least four. For purposes of illustration and notlimitation, a third tap weight coefficient C₃ and a fourth tap weightcoefficient C₄ of the first means for filtering can be constrained. Theinformation communication system can include means for updating Δθaccording to the equation:

${{\Delta\;\theta} = \frac{\left( {{{- \Delta}\; C_{3}*K_{e}} - {\Delta\; C_{4}*K_{o}}} \right)}{K_{e}^{2} + K_{o}^{2}}},$wherein ΔC₃ and ΔC₄ are updated according to the equations:ΔC ₃ =μ*E[n]*X[n−3] andΔC ₄ =μ*E[n]*X[n−4], respectively,wherein μ comprises a second gain constant, E[n] comprises an errorsignal for the current sampling time of the input signal, X[n−3]comprises the value of the input signal at the third previous samplingtime of the input signal, and X[n−4] comprises the value of the inputsignal at the fourth previous sampling time of the input signal.According to the third aspect, the means for updating the tap weightcoefficients can include means for updating K_(e) and K_(o) according tothe equations:

${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$and

${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$respectively,wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1”otherwise, M can be determined according to the equation:M=TRUNCATE((N−1)/2), andP can be determined according to the equation:P=TRUNCATE(((N−1)/2)−0.5).According to an alternative exemplary embodiment of the third aspect,K_(e) and K_(o) can each comprise a predetermined value.

According to the third aspect, the information communication system caninclude means for detecting an information sequence in the firstfiltered signal. The means for detecting can be responsive to an outputof the first means for filtering. The information communication systemcan include means for reconstructing an information signal from theinformation sequence. The means for reconstructing can be responsive toan output of the means for detecting. The information communicationsystem can also include means for generating an error signal. The meansfor generating an error signal can be responsive to the output of thefirst means for filtering and an output of the means for reconstructing.The means for generating an error signal can generate the error signalE[n] comprising a difference between the output of the first means forfiltering and the output of the means for reconstructing.

According to an alternative exemplary embodiment of the third aspect,the first means for filtering can comprise N tap weight coefficients,wherein N comprises at least four. For purposes of illustration and notlimitation, a third tap weight coefficient C₃ and a fourth tap weightcoefficient C₄ of the first means for filtering can be constrained. Themeans for updating tap weight coefficients can include means forupdating Δθ according to the equation:Δθ=(−ΔC ₃ *K _(e) −ΔC ₄ *K _(o)),wherein ΔC₃ and ΔC₄ are updated according to the equations:ΔC ₃ =μ*E[n]*X[n−3] andΔC₄ =μ*E[n]*X[n−4], respectively,wherein μ comprises a second gain constant, E[n] comprises an errorsignal for the current sampling time of the input signal, X[n−3]comprises the value of the input signal at the third previous samplingtime of the input signal, and X[n−4] comprises the value of the inputsignal at the fourth previous sampling time of the input signal.According to the third aspect, the means for updating the tap weightcoefficients can include means for updating K_(e) and K_(o) according tothe equations:

${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$and

${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$respectively,wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1”otherwise, M can be determined according to the equation:M=TRUNCATE((N−1)/2), andP can be determined according to the equation:P=TRUNCATE(((N−1)/2)−0.5).According to an alternative exemplary embodiment of the third aspect,K_(e) and K_(o) can each comprise a predetermined value. The means forgenerating an error signal can generate the error signal E[n] comprisinga difference between the output of the first means for filtering and theoutput of the means for reconstructing.

According to the third aspect, the information communication system caninclude means for updating the tap weight coefficient “b” according tothe equation:b[n+1]=b[n]−β*ΔΓ,wherein b[n+1] comprises the value of the tap weight coefficient “b” forthe next sampling time of the input signal, b[n] comprises the value ofthe tap weight coefficient “b” for the current sampling time of theinput signal, β comprises a first gain constant, and ΔΓ comprises thechange in gain error from the first means for filtering. According to anexemplary embodiment of the third aspect, the first means for filteringcan comprise N tap weight coefficients, wherein N comprises at leastfour. For purposes of illustration and not limitation, a third tapweight coefficient C₃ and a fourth tap weight coefficient C₄ of thefirst means for filtering can be constrained. The means for updating thetap weight coefficient can include means for updating ΔΓ according toequation:

${{\Delta\Gamma} = \frac{\left( {{{- \Delta}\; C_{3}*K_{o}} + {\Delta\; C_{4}*K_{e}}} \right)}{\sqrt{K_{e}^{2} + K_{o}^{2}}}},$wherein ΔC₃ and ΔC₄ are updated according to the equations:ΔC ₃ =μ*E[n]*X[n−3] andΔC ₄ =μ*E[n]*X[n−4], respectively,wherein μ comprises a second gain constant, E[n] comprises an errorsignal for the current sampling time of the input signal, X[n−3]comprises the value of the input signal at the third previous samplingtime of the input signal, and X[n−4] comprises the value of the inputsignal at the fourth previous sampling time of the input signal.According to the third aspect, the means for updating the tap weightcoefficient can include means for updating K_(e) and K_(o) according tothe equations:

${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$and

${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$respectively,wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1”otherwise, M can be determined according to the equation:M=TRUNCATE((N−1)/2), andP can be determined according to the equation:P=TRUNCATE(((N−1)/2)−0.5).According to an alternative exemplary embodiment of the third aspect,K_(e) and K_(o) can each comprise a predetermined value. The means forgenerating an error signal generates the error signal E[n] comprising adifference between the output of the first means for filtering and theoutput of the means for reconstructing.

According to an alternative exemplary embodiment of the third aspect,the first means for filtering can comprise N tap weight coefficients,wherein N comprises at least four. For purposes of illustration and notlimitation, a third tap weight coefficient C₃ and a fourth tap weightcoefficient C₄ of the first means for filtering can be constrained. Themeans for updating the tap weight coefficient can include means forupdating ΔΓ according to the equation:ΔΓ=(−ΔC ₃ *K _(o) +ΔC ₄ *K _(e)),wherein ΔC₃ and ΔC₄ are updated according to the equations:ΔC ₃ =μ*E[n]*X[n−3] andΔC ₄ =μ*E[n]*X[n−4], respectively,wherein μ comprises a second gain constant, E[n] comprises an errorsignal for the current sampling time of the input signal, X[n−3]comprises the value of the input signal at the third previous samplingtime of the input signal, and X[n−4] comprises the value of the inputsignal at the fourth previous sampling time of the input signal.According to the third aspect, the means for updating the tap weightcoefficient can include means for updating K_(e) and K_(o) according tothe equations:

${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$and

${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$respectively,wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1”otherwise, M can be determined according to the equation:M=TRUNCATE((N−1)/2), andP can be determined according to the equation:P=TRUNCATE(((N−1)/2)−0.5).According to an alternative exemplary embodiment of the third aspect,K_(e) and K_(o) can each comprise a predetermined value. The means forgenerating an error signal generates the error signal E[n] comprising adifference between the output of the first means for filtering and theoutput of the means for reconstructing.

According to the third aspect, the information communication system caninclude means for generating an error signal. The means for generatingan error signal can be responsive to the output of the means forreconstructing. The means for generating an error signal can be incommunication between an output of the second means for filtering andinputs of the means for controlling the gain and the means forcontrolling the timing phase. The first means for filtering and thesecond means for filtering can each comprise a FIR filter means.According to an exemplary embodiment of the third aspect, a disk drivemeans can comprise the information communication system. At least themeans for amplifying, the means for converting, the first means forfiltering, the second means for filtering, and at least one of the meansfor controlling a gain of the means for amplifying and the means forcontrolling a timing phase of the means for converting can be formed ona monolithic substrate. The information communication system can becompliant with a standard selected from the group consisting of 802.11,802.11a, 802.11b, 802.11g and 802.11i.

According to a fourth aspect of the present invention, an informationcommunication system includes a variable gain amplifier (VGA) responsiveto an input signal of the information communication system. Theinformation communication system includes an analog-to-digital converter(ADC) responsive to an output of the VGA. The information communicationsystem includes a first filter responsive to an output of the ADC. Tapweight coefficients of the first filter can be updated according to afirst least mean square (LMS) engine. At least one tap weightcoefficient of the first filter can be constrained. The informationcommunication system includes a second filter responsive to an output ofthe first filter. The number of tap weight coefficients of the secondfilter can be less than or equal to the number of the tap weightcoefficients of the first filter. The information communication systemincludes a gain controller for controlling gain of the VGA. The gaincontroller is in communication with the VGA and responsive to the outputof the second filter.

According to a fifth aspect of the present invention, an informationcommunication system includes a variable gain amplifier (VGA) responsiveto an input signal of the information communication system. Theinformation communication system includes an analog-to-digital converter(ADC) responsive to an output of the VGA. The information communicationsystem includes a first filter responsive to an output of the ADC. Tapweight coefficients of the first filter can be updated according to afirst least mean square (LMS) engine. At least one tap weightcoefficient of the first filter can be constrained. The informationcommunication system includes a second filter responsive to an output ofthe first filter. The number of tap weight coefficients of the secondfilter can be less than or equal to the number of the tap weightcoefficients of the first filter. The information communication systemincludes a timing phase controller for controlling timing phase of theADC. The timing phase controller can be in communication with the ADCand responsive to an output of the second filter.

According to a sixth aspect of the present invention, an informationcommunication system includes means for amplifying an input signalreceived by the information communication system to generate anamplified signal. The information communication system includes meansfor converting the amplified signal into a digital signal to generate aconverted signal. The information communication system includes firstmeans for filtering the converted signal to generate a first filteredsignal. Tap weight coefficients of the first means for filtering can beupdated according to a first least mean square (LMS) adaptation means.At least one tap weight coefficient of the first means for filtering canbe constrained. The information communication system includes secondmeans for filtering the first filtered signal to generate a secondfiltered signal. The number of tap weight coefficients of the secondmeans for filtering can be less than or equal to a number of the tapweight coefficients of the first means for filtering. The informationcommunication system includes means for controlling a gain of the meansfor amplifying in response to the second filtered signal.

According to a sixth aspect of the present invention, an informationcommunication system includes means for amplifying an input signalreceived by the information communication system to generate anamplified signal. The information communication system includes meansfor converting the amplified signal into a digital signal to generate aconverted signal. The information communication system includes firstmeans for filtering the converted signal to generate a first filteredsignal. Tap weight coefficients of the first means for filtering can beupdated according to a first least mean square (LMS) adaptation means.At least one tap weight coefficient of the first means for filtering canbe constrained. The information communication system includes secondmeans for filtering the first filtered signal to generate a secondfiltered signal. The number of tap weight coefficients of the secondmeans for filtering can be less than or equal to a number of the tapweight coefficients of the first means for filtering. The informationcommunication system includes means for controlling a timing phase ofthe means for converting in response to the second filtered signal.

According to a seventh aspect of the present invention, a computerprogram for controlling at least one of gain and timing phase performsthe steps of: a.) filtering an input signal to generate a first filteredsignal in accordance with a first plurality of filter coefficients; b.)updating the first plurality of filter coefficients according to a firstleast mean square (LMS) process; c.) constraining at least one filtercoefficient of the first plurality of filter coefficients; d.) filteringthe first filtered signal to generate a second filtered signal inaccordance with a second plurality of filter coefficients, wherein thenumber of filter coefficients of the second plurality of filtercoefficients can be less than or equal to the number of the filtercoefficients of the first plurality of filter coefficients; e.)outputting a gain control signal in response to the second filteredsignal; and f.) outputting a timing phase control signal in response tothe second filtered signal.

BRIEF DESCRIPTION OF THE DRAWINGS

Other objects and advantages of the present invention will becomeapparent to those skilled in the art upon reading the following detaileddescription of preferred embodiments, in conjunction with theaccompanying drawings, wherein like reference numerals have been used todesignate like elements, and wherein:

FIG. 1 is a block diagram illustrating a system for controlling gain andtiming phase in the presence of a first filter using a second filter, inaccordance with an exemplary embodiment of the present invention.

FIG. 2 is a functional block diagram of a disk drive system, inaccordance with an exemplary embodiment of the present invention.

FIGS. 3A and 3B are flowcharts illustrating steps for controlling atleast one of gain and timing phase, in accordance with an exemplaryembodiment of the present invention.

FIG. 4 is a flowchart illustrating steps for updating a filtercoefficient “a” of a second plurality of filter coefficients, inaccordance with an exemplary embodiment of the present invention.

FIG. 5 is a flowchart illustrating steps for updating a filtercoefficient “a” of a second plurality of filter coefficients, inaccordance with an alternative exemplary embodiment of the presentinvention.

FIG. 6 is a flowchart illustrating steps for updating a filtercoefficient “b” of a second plurality of filter coefficients, inaccordance with an exemplary embodiment of the present invention.

FIG. 7 is a flowchart illustrating steps for updating a filtercoefficient “b” of a second plurality of filter coefficients, inaccordance with an alternative exemplary embodiment of the presentinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Exemplary embodiments of the present invention are directed to a systemand method for controlling gain and timing phase in the presence of afirst Least Mean Square (LMS) filter using a second adaptive filter.According to exemplary embodiments, in an information communicationsystem, such as, for example, a receiver, a disk drive or the like, asimple secondary filter, having tap weight coefficients updatedaccording to an adaptive algorithm such as, for example, a LMSalgorithm, can be added after a primary filter, having tap weightcoefficients updated according to a LMS algorithm. At least one tapweight coefficient of the primary filter can be constrained or otherwisenot adapted. The simple secondary filter can be added in the loop thatimplements the gain control and timing phase control of the informationcommunication system. The simple secondary filter can be, for example, atwo-tap filter or a three-tap filter. According to exemplaryembodiments, the tap weight coefficients of the three-tap filter can be(a, 1+b, −a), and the tap weight coefficients of the two-tap filter canbe (a, 1+b).

The simple secondary filter can introduce a slight gain differencebetween the output of the primary filter and the output of the simplesecondary filter to allow the gain control mechanism and the LMSalgorithm used to update the tap weight coefficients of the primaryfilter to each receive the signal amplitude level that each requires foroptimal performance. In other words, the tap weight coefficient “b” ofthe simple secondary filter can be adapted to account for the change ingain that is “missing” from the LMS adaptation of the tap weightcoefficients of the primary filter resulting from the constrained tapweight coefficients. In addition, by using a simple secondary filter,instead of, for example, a gain stage, a slight sampling phase offsetcan be introduced between the output of the primary filter and theoutput of the simple secondary filter. In other words, the tap weightcoefficient “a” of the simple secondary filter can be adapted to accountfor the change in timing phase error associated with the primary filteras a result of the constrained tap weight coefficients. The slightsampling phase offset can be used to compensate for any bias in thetiming phase recovery.

These and other aspects of the present invention will now be describedin greater detail. FIG. 1 is a block diagram illustrating a system forcontrolling gain and timing phase in the presence of a first filterusing a second filter, in accordance with an exemplary embodiment of thepresent invention. An information communication system 100 includes avariable gain amplifier (VGA) 105. VGA 105 is responsive to an inputsignal 103 to the information communication system 100. The informationcommunication system 100 includes an analog-to-digital converter (ADC)110. ADC 110 is responsive to an output of VGA 105.

The information communication system 100 includes a first filter 115.According to exemplary embodiments, the tap weight coefficients of firstfilter 115 are updated according to a first LMS engine 113. The firstfilter 115 can be, for example, a Finite Impulse Response (FIR) filter,an Infinite Impulse Response (IIR) filter, or any other suitable type offilter that can use first LMS engine 113 to update the tap weightcoefficients of the filter according to the LMS algorithm. First filter115 can be of any length (i.e., can include any desired number of tapweight coefficients), depending on, for example, the characteristics ofthe communicated information, the channel through which the informationis communicated, the environment and application in which theinformation communication system 100 is used, and the like. First filter115 is responsive to an output of ADC 110.

The information communication system 100 can include a sequence detector135. For example, sequence detector 135 can be a Viterbi detector or thelike. Sequence detector 135 is responsive to an output of first filter115. The information communication system 100 can include areconstruction filter 140. Reconstruction filter 140 is responsive to anoutput of sequence detector 135. According to an exemplary embodiment,the first LMS engine 113 is responsive to the output of ADC 110 and toan error signal generated by error generator 119. The error generator119 is responsive to the output of first filter 115 and an output of thereconstruction filter 140. The error generator 119 generates an errorsignal comprising the difference between the output of first filter 115and the output of the reconstruction filter 140.

The information communication system 100 includes a second filter 120.According to exemplary embodiments, the tap weight coefficients ofsecond filter 120 are updated according to an adaptation engine 117. Theadaptation engine 117 can comprise, for example, a second LMS engine, azero-forcing engine or any other suitable type of adaptive filterengine. According to an exemplary embodiment, the adaptation engine 117can be responsive to the input of second filter 120 and the output ofsecond filter 120. The second filter 120 can be, for example, a FIRfilter, an IIR filter, or any other suitable type of filter that can useadaptation engine 117 to update the tap weight coefficients of thefilter according to an adaptive algorithm. According to an exemplaryembodiment, the complexity of the second filter 120 is less than orequal to the complexity of the first filter 115. In other words, thenumber of tap weight coefficients of the second filter 120 is less thanor equal to the number of tap weight coefficients of the first filter115. However, second filter 120 can be of any length (i.e., can includeany desired number of tap weight coefficients), depending on, forexample, the characteristics of the communicated information, thechannel through which the information is communicated, the environmentand application in which information communication system 100 is used,and the like. Second filter 120 is responsive to an output of the firstfilter 115.

The information communication system 100 can include a gain controller125 for controlling the gain of VGA 105. According to an exemplaryembodiment, gain controller 125 can be a Zero-Forcing (ZF) AutomaticGain Control (AGC) or any other suitable type of AGC. Gain controller125 is responsive to an output of the second filter 120. Gain controller125 is in communication with VGA 105. Additionally or alternatively togain controller 125, information communication system 100 can include atiming phase controller 130 for controlling the timing phase of ADC 110.Timing phase controller 130 is responsive to an output of the secondfilter 120. Timing phase controller 130 is in communication with ADC110.

If the tap weight coefficients of first filter 115 are updated accordingto first LMS engine 113 using an unconstrained LMS algorithm, all tapweight coefficients of first filter 115 are adapted and the coefficientscan converge to values that minimize the Mean Square Error (MSE) of thesignal output by first filter 115 (assuming, for example, that gaincontrol and timing phase recovery are stable). To remove the interactionbetween the LMS algorithm used to update the tap weight coefficients ofthe first filter 115 and the gain control and timing phase recoveryalgorithms used to control the VGA 105 and ADC 110, respectively, theLMS algorithm used to update the tap weight coefficients of first filter115 (through first LMS engine 113) can be constrained in at least twodimensions. Conventionally, to provide the desired isolation between theLMS algorithm used to update the tap weight coefficients of first filter115 and the gain control and timing phase recovery, two or more tapweight coefficients of the first filter 115 can be constrained orotherwise not adapted so as not to participate in the LMS adaptationprocess. According to an exemplary embodiment of the present invention,at least one tap weight coefficient of the first filter 115 can beconstrained, although any desired number of tap weight coefficients ofthe first filter 115 can be constrained or otherwise not adapted.

According to an exemplary embodiment of the present invention, at leasttwo tap weight coefficients of first filter 115 are constrained.Consequently, the value of at least one tap weight coefficient of thesecond filter 120 is updated to provide a gain of the second filter 120that is associated with a change in gain error from the first filter115. The gain of the second filter 120 is configured to cause the gaincontroller 125 to modify a gain of VGA 105 to compensate for the changein gain error from the first filter 115. In addition, the value of atleast one tap weight coefficient of the second filter 120 is updated toprovide a timing phase of the second filter 120 that is associated witha change in timing phase error introduced by the first filter 115. Thetiming phase of the second filter 120 is configured to cause the timingphase controller 130 to modify the timing phase of ADC 110 to compensatefor the change in timing phase error introduced by the first filter 115.

According to exemplary embodiments, second filter 120 can comprise, forexample, a two-tap filter or a three-tap filter, although filters ofother lengths can be used, with the tap weight coefficients of thefilter updated according to an adaptive algorithm. For example, the tapweight coefficients of the two-tap filter can comprise “a” and “1+b”,respectively. The tap weight coefficients of the three-tap filter cancomprise “a”, “1+b”, and “−a”, respectively. According to an exemplaryembodiment, the values of tap weight coefficients “a” and “b” can be setat predetermined values. However, the values of the tap weightcoefficients “a” and “b” can be adapted. To adapt the tap weightcoefficients “a” and “b”, a characteristic gain of the first filter 115is defined. Generally, the gain of a FIR filter, having tap weightcoefficients updated according to a LMS algorithm, is a function offrequency. For example, for a magnetic recording application or thelike, the signal energy is concentrated around approximately one-halfthe Nyquist frequency of the system.

Consequently, the characteristic gain of the first filter 115 is definedto be the gain of the first filter 115 at one-half of the Nyquistfrequency, as described by Equation (2):Γ=√{square root over (K _(e) ² +K _(o) ²)}.  (2)In Equation (2), K_(e) is defined according to Equation (3):

$\begin{matrix}{K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}} & (3)\end{matrix}$where γ=+1 when ((2*n) modulo 4)=0, and γ=−1 otherwise. In Equation (3),each tap weight coefficient C_(2n) represents the value of an even tapweight coefficient (e.g., C₀ is the value of the zeroeth tap weightcoefficient, C₂ is the value of the second tap weight coefficient,etc.). If the first filter 115 is comprised of N tap weightcoefficients, M is determined according to Equation (4):M=TRUNCATE((N−1)/2).  (4)According to exemplary embodiments, the TRUNCATE function truncates thegiven number to its integer portion, discarding any fractional part.Thus, for example, TRUNCATE(2.9)=2, TRUNCATE(2.5)=2, and TRUNCATE(2)=2.According to Equation (3), therefore, K_(e)=C₀−C₂+C₄−C₆ . . . , with thelength of the resulting equation (and, consequently, the value of K_(e))depending upon the total number of (even) tap weight coefficients offirst filter 115.

In Equation (2), K_(o) is defined according to Equation (5):

$\begin{matrix}{K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}} & (5)\end{matrix}$where γ=+1 when ((2*n) modulo 4)=0, and γ=−1 otherwise. In Equation (5),each tap weight coefficient C_(2n+1) represents the value of an odd tapweight coefficient (e.g., C₁ is the value of the first tap weightcoefficient, C₃ is the value of the third tap weight coefficient, etc.).If the first filter 115 is comprised of N tap weight coefficients, P isdetermined according to Equation (6):P=TRUNCATE(((N−1)/2)−0.5).  (6)According to Equation (5), therefore, K_(o)=C₁−C₃+C₅−C₇ . . . , with thelength of the resulting equation (and, consequently, the value of K_(o))depending upon the total number of (odd) tap weight coefficients offirst filter 115. According to an alternative exemplary embodiment,highly quantized values of K_(e) and K_(o) (e.g., +1 or −1, or any othersuitable values) can be used instead of the values calculated accordingto Equations (3) and (5), respectively.

As noted previously, to isolate adaptation of the LMS algorithm used toupdate the tap weight coefficients of first filter 115 (through firstLMS engine 113) from gain controller 125 and timing phase controller130, two or more of the tap weight coefficients of first filter 115 areconstrained. However, constraining the tap weight coefficients canresult in the loss of the change in gain that the constrained tap weightcoefficients would have contributed. According to exemplary embodiments,the first filter 115 can comprise N tap weight coefficients, where N cancomprise at least four, although N can be any number greater than zero.According to an exemplary embodiment, a third tap weight coefficient C₃and a fourth tap weight coefficient C₄ of the first filter 115 areconstrained, although additional and/or alternative tap weightcoefficients can be constrained. For purposes of illustration and notlimitation, if C₃ and C₄ are the constrained tap weight coefficients,then the missing gain change is represented by Equation (7):

$\begin{matrix}{{\Delta\Gamma} = {\frac{\left( {{{- \Delta}\; C_{3}*K_{o}} + {\Delta\; C_{4}*K_{e}}} \right)}{\Gamma}.}} & (7)\end{matrix}$In Equation (7), ΔC₃ is updated according to Equation (8), and ΔC₄ isupdated according to Equation (9), as follows:ΔC ₃ =μ*E[n]*X[n−3]  (8)ΔC ₄ =μ*E[n]*X[n−4].  (9)In Equations (8) and (9), μ comprises a gain constant or step-sizeparameter and can be any suitable value, such as, for example, any valuebetween zero and one or any appropriate value. E[n] comprises an errorsignal for the current sampling time of the input signal 103,representing the difference between the output of the first filter 115and the output of the reconstruction filter 140. X[n−3] comprises thevalue of the input signal 103 at a third previous (time-delayed)sampling time of the input signal 103, and X[n−4] comprises the value ofthe input signal 103 at a fourth previous (time-delayed) sampling timeof the input signal 103.

In Equation (7), ΔΓ represents the change in gain error from theadaptation of the LMS algorithm used to update the tap weightcoefficients of first filter 115 due to the constraint of tap weightcoefficients C₃ and C₄. Equation (7) can be modified to represent thegain change error due to the constraint of additional and/or alternativetap weight coefficients. For example, if more than two tap weightcoefficients are constrained, Equation (7) can include the ΔC term(s)for the additional tap weight coefficients, with the polarity of each ΔCterm corresponding to the polarity of the tap weight coefficient asrepresented in Equations (3) and (5) for K_(e) and K_(o), respectively.In addition, common terms that are nearly constant or are large inmagnitude can be dropped from Equation (7). Consequently, for purposesof illustration and not limitation, the following simplified equationrepresents the gain change error resulting from the constraint of tapweight coefficients C₃ and C₄ of first filter 115:ΔΓ=(−ΔC ₃ *K _(o) +ΔC ₄ *K _(e))  (10)In Equation (10), ΔC₃ and ΔC₄ are updated according to Equations (8) and(9), respectively, and K_(e) and K_(o) are updated according toEquations (3) and (5), respectively.

The gain change error ΔΓ can cause the improper functioning of, forexample, a ZF AGC algorithm in the presence of the constrained LMSalgorithm used to update the tap weight coefficients of the first filter115. According to exemplary embodiments, to allow the LMS algorithm usedto update the tap weight coefficients of the first filter 115 toconverge properly, the amplitude of the signal input to first filter 115can be adjusted. For example, if ΔΓ is positive, then the amplitude ofthe output of VGA 105 can be increased to compensate for the amount ofthe gain change error. According to exemplary embodiments, thecompensation can be accomplished by, for example, reducing the gain ofthe second filter 120 by the amount −ΔΓ. This reduction in the amplitudeof the signal output by second filter 120 causes the gain controller 125to increase the gain of VGA 105 by the corresponding amount. Theresultant higher gain value of VGA 105 results in an increase to thesignal amplitude of input signal 103, thereby increasing the signalamplitude of the signal output by first filter 115.

Thus, according to exemplary embodiments, the tap weight coefficient “b”of second filter 120 is updated according to Equation (11):b[n+1]=b[n]−β*ΔΓ  (11)In Equation (11), b[n+1] comprises the value of the tap weightcoefficient “b” for the next sampling time of the input signal 103,while b[n] comprises the value of the tap weight coefficient “b” for thecurrent sampling time of the input signal 103. The gain constant β canbe any suitable value, such as, for example, any value between zero andone or any appropriate value. The gain change error from the firstfilter 115, ΔΓ, is determined according to, for example, Equation (7),Equation (10) or a modified version of either Equation (7) or Equation(10) that accounts for additional and/or alternative constrained tapweight coefficients of first filter 115.

Additionally, there can be a timing phase rotation or error as a resultof the constrained LMS algorithm used to update the tap weightcoefficients of first filter 115. For example, for a signal componentlocated at approximately one-half the Nyquist frequency of the system,the timing phase rotation or error introduced by the LMS algorithm usedto update the tap weight coefficients of first filter 115 can beconsidered substantially equivalent to the timing phase rotation orerror for a two-tap filter with tap weight coefficients (K_(e), K_(o)).The phase angle for such a filter at approximately one-half the Nyquistfrequency would be TAN⁻¹(K_(o)/K_(e)). According to exemplaryembodiments, the first filter 115 can comprise N tap weightcoefficients, where N can comprise at least four, although N can be anynumber greater than zero. According to the exemplary embodiment, a thirdtap weight coefficient C₃ and a fourth tap weight coefficient C₄ of thefirst filter 115 are constrained, although additional and/or alternativetap weight coefficients can be constrained. For purposes of illustrationand not limitation, if C₃ and C₄ are the constrained tap weightcoefficients, then the timing phase error introduced by first filter 115is represented by Equation (12):

$\begin{matrix}{{\Delta\theta} = {\frac{\left( {{{- \Delta}\; C_{3}*K_{e}} - {\Delta\; C_{4}*K_{o}}} \right)}{K_{e}^{2} + K_{o}^{2}}.}} & (12)\end{matrix}$In Equation (12), ΔC₃ is updated according to Equation (8), ΔC₄ isupdated according to Equation (9), and K_(e) and K_(o) is updatedaccording to Equations (3) and (5), respectively.

In Equation (12), Δθ represents the change in timing phase error thathas been introduced by the LMS algorithm used to update the tap weightcoefficients of first filter 115 due to the constraint of tap weightcoefficients C₃ and C₄. Equation (12) can be modified to represent thechange in timing phase error due to the constraint of additional and/oralternative tap weight coefficients. For example, if more than two tapsare constrained, Equation (12) can include the ΔC term(s) for theadditional tap weight coefficients. In addition, common terms that arenearly constant or are large in magnitude can be dropped from Equation(12). Consequently, for purposes of illustration and not limitation, thefollowing simplified equation represents the timing phase errorresulting from the constraint of tap weight coefficients C₃ and C₄ offirst filter 115:Δθ=(−ΔC ₃ *K _(e) −ΔC ₄ *K _(o))  (13)In Equation (13), ΔC₃ and ΔC₄ are updated according to Equations (8) and(9), respectively, and K_(e) and K_(o) are updated according toEquations (3) and (5), respectively.

According to exemplary embodiments, to allow the LMS algorithm used toupdate the tap weight coefficients of the first filter 115 to convergeproperly, the timing phase of the signal input to first filter 115 isadjusted. For example, if Δθ is positive, then the timing phase of thesignal output by ADC 110 is shifted or otherwise adjusted to compensatefor the amount of the timing phase error. According to exemplaryembodiments, the compensation can be accomplished by, for example,rotating or otherwise adjusting the timing phase of the second filter120 by the amount −Δθ. This rotation in the timing phase of the signaloutput by second filter 120 causes the timing phase controller 130 torotate or otherwise adjust the timing phase of ADC 110 in the oppositedirection by a corresponding amount. The resultant timing phase rotationor adjustment of ADC 110 results in a rotation of the timing phase ofinput signal 103, thereby rotating or adjusting the timing phase of thesignal output by first filter 115.

Thus, according to exemplary embodiments, the tap weight coefficient “a”of second filter 120 is updated according to Equation (14):a[n+1]=a[n]−α*Δθ,  (14)In Equation (14), a[n+1] comprises the value of the tap weightcoefficient “a” for the next sampling time of the input signal 103,while a[n] comprises the value of the tap weight coefficient “a” for thecurrent sampling time of the input signal 103. The gain constant α canbe any suitable value, such as, for example, any value between zero andone or any appropriate value. The change in timing phase errorassociated with first filter 115, Δθ, is determined according to, forexample, Equation (12), Equation (13) or a modified version of eitherEquation (12) or Equation (13) that accounts for additional and/oralternative constrained tap weight coefficients of first filter 115.

According to an exemplary embodiment, information communication system100 can optionally include an error generator 145. Error generator 145is responsive to the output of reconstruction filter 140. Errorgenerator 145 is in communication with an output of second filter 120and inputs of either or both gain controller 125 and timing phasecontroller 130. According to an alternative exemplary embodiment,instead of a separate error generator 145, gain controller 125 caninclude an error generator. Gain controller 125 can then be responsiveto the output of reconstruction filter 140. According to the alternativeexemplary embodiment, timing phase controller 130 can also include anerror generator, instead of a separate error generator 145.Consequently, timing phase controller 130 can also be responsive to theoutput of reconstruction filter 140.

According to a preferred embodiment of the present invention, a diskdrive can comprise the information communication system 100. FIG. 2 is afunctional block diagram of a disk drive system 200, in accordance withan exemplary embodiment of the present invention. The disk drive system200 includes a disk drive 205 that can be of, for example, a 2-, 4- or8-channel configuration or any other suitable configuration. The diskdrive 205 is comprised of a hard disk controller (HDC) 210 thatinterfaces with a host device, such as a host computer 215, and furtherincludes a microprocessor 220 and memory 225, each in communication withthe HDC 210. A motor driver 230 is also provided. Disk drive 205 alsoincludes a read channel 235, the output of which is supplied to the HDC210. A pre-amplifier integrated circuit 240 generates an output signalthat is supplied as an input to the read channel 235. The pre-amplifieris in communication with a recording head 245, which can be, for examplea Magneto-Resistive (MR) or Giant Magneto-Resistive (GMR) recording heador any other suitable recording head. For example, exemplary embodimentsof the present invention can be used in or by, for example, read channel235 or any other suitable component of disk drive system 200, and/or canbe performed by the combination of microprocessor 220 and memory 225.

Additionally, exemplary embodiments of the present invention can beused, for example, for communicating information over noisycommunication channels and the like. For example, informationcommunication system 100 can be compliant with a standard selected fromthe group consisting of 802.11, 802.11a, 802.11b, 802.11g and 802.11i,or any other suitable wired or wireless standard. However, informationcommunication system 100 can be used in any device or system thatcommunicates information, including both wired and wirelesscommunication systems, read channel devices, disk drive systems (e.g.,those employing read channel devices), other magnetic storage orrecording applications, and the like, particularly in systems anddevices where a substantial portion of the signal energy in thecommunicated information signal is located at approximately one-half ofthe Nyquist frequency of the system.

The input signal 103 can be any suitable type of electrical signal thatis capable of communicating electrical information. VGA 105, ADC 110,first filter 115, first LMS engine 113, error generator 119, secondfilter 120, adaptation engine 117, gain controller 125, timing phasecontroller 130, sequence detector 135, reconstruction filter 140 anderror generator 145 can each be implemented using any suitable means forperforming the functions associated with the respective element. VGA105, ADC 110, first filter 115, first LMS engine 113, error generator119, second filter 120, adaptation engine 117, gain controller 125,timing phase controller 130, sequence detector 135, reconstructionfilter 140 and error generator 145, or any combination thereof, can beformed on, for example, a monolithic substrate. Alternatively, eachelement, or any combination thereof, can be any suitable type ofelectrical or electronic component or device that is capable ofperforming the functions associated with the respective element.According to such an alternative exemplary embodiment, each component ordevice can be in communication with another component or device usingany appropriate type of electrical connection that is capable ofcarrying electrical information.

Those of ordinary skilled will recognize that the informationcommunication system 100 can include any additional electrical orelectronic components, devices or elements that can be used forcommunicating information signals, including mixers, local oscillators,demodulators, modulators, phase locked loops, power amplifiers, powersupplies, additional filters, or any other appropriate components,devices or elements in any suitable combination that can be used forcommunicating information signals, depending upon the nature and type ofinformation signals to be communicated and the environment in which theinformation communication system 100 is to be used. For example, theinformation communication system 100 can form the receiver portion of atransceiver system for transmitting and receiving information, can formportion of a disk drive or other magnetic storage or recording device,or the like.

FIGS. 3A and 3B are flowcharts illustrating steps for controlling atleast one of gain and timing phase, in accordance with an exemplaryembodiment of the present invention. In step 305 of FIG. 3A, an inputsignal is amplified to generate an amplified signal. In step 310, theamplified signal is converted into a digital signal to generate aconverted signal.

In step 315, the converted signal is filtered to generate a firstfiltered signal in accordance with a first plurality of filtercoefficients. The first plurality of filter coefficients are updatedaccording to a first LMS process. The first plurality of filtercoefficients can be of any number (i.e., can include any desired numberof filter coefficients). According to exemplary embodiments, at leastone filter coefficient of the first plurality of filter coefficients canbe constrained. For example, two or more filter coefficients of thefirst plurality of filter coefficients can be constrained.

In step 320, the first filtered signal is filtered to generate a secondfiltered signal in accordance with a second plurality of filtercoefficients. For example, the second plurality of filter coefficientscan be updated according to an adaptation process, such as, for example,a second LMS process, a zero-forcing process, or any other suitableadaptation process. According to exemplary embodiments, the number offilter coefficients of the second plurality of filter coefficients isless than or equal to the number of the filter coefficients of the firstplurality of filter coefficients. For example, the second plurality offilter coefficients can comprise two or three filter coefficients.However, the second plurality of filter coefficients can be of anynumber (i.e., can include any desired number of filter coefficients).

In step 325, a value of at least one filter coefficient of the secondplurality of filter coefficients is updated to provide a timing phase ofStep 320 that is associated with a change in timing phase errorintroduced by Step 315. According to exemplary embodiments, the twofilter coefficients of the second plurality of filter coefficients cancomprise “a” and “1+b”, respectively, and the three filter coefficientsof the second plurality of filter coefficients can comprise “a”, “1+b”,and “−a”, respectively. In step 330, the filter coefficient “a” of thesecond plurality of filter coefficients is updated according to Equation(14). In step 335, a value of at least one filter coefficient of thesecond plurality of filter coefficients is updated to provide a gain ofStep 320 that is associated with a change in gain error from Step 315.In step 340, the filter coefficient “b” of the second plurality offilter coefficients is updated according to Equation (11).

In step 345 of FIG. 3B, a gain of Step 305 is controlled in response tothe second filtered signal. In step 350, a gain of Step 305 is modifiedbased upon the gain of Step 320, to compensate for the change in gainerror from Step 315. In step 355, a timing phase of Step 310 iscontrolled in response to the second filtered signal. In step 360, atiming phase of Step 310 is modified based upon the timing phase of Step320, to compensate for the change in timing phase error introduced byStep 315.

In step 365, an information sequence is detected in the first filteredsignal. In step 370, an information signal is reconstructed from thedetected information sequence. In step 375, an error signal is generatedthat comprises a difference between the first filtered signal and thereconstructed information signal.

FIG. 4 is a flowchart illustrating steps for updating a filtercoefficient “a” of the second plurality of filter coefficients, inaccordance with an exemplary embodiment of the present invention.According to an exemplary embodiment, the first plurality of filtercoefficients can comprise N filter coefficients, wherein N comprises atleast four, although N can be any number greater than zero. For example,a third filter coefficient C₃ and a fourth filter coefficient C₄ of thefirst plurality of filter coefficients can be constrained. In step 405,Δθ is updated according to Equation (12). In step 410, K_(e) and K_(o)are updated according to Equations (3) and (5), respectively. Accordingto an alternative exemplary embodiment, K_(e) and K_(o) can eachcomprise a predetermined value.

FIG. 5 is a flowchart illustrating steps for updating a filtercoefficient “a” of the second plurality of filter coefficients, inaccordance with an alternative exemplary embodiment of the presentinvention. In step 505, Δθ is updated according to Equation (13). Instep 510, K_(e) and K_(o) are updated according to Equations (3) and(5), respectively. According to an alternative exemplary embodiment,K_(e) and K_(o) can each comprise a predetermined value.

FIG. 6 is a flowchart illustrating steps for updating a filtercoefficient “b” of the second plurality of filter coefficients, inaccordance with an exemplary embodiment of the present invention.According to an exemplary embodiment, the first plurality of filtercoefficients can comprise N filter coefficients, wherein N comprises atleast four, although N can be any number greater than zero. For example,a third filter coefficient C₃ and a fourth filter coefficient C₄ of thefirst plurality of filter coefficients can be constrained. In step 605,ΔΓ is updated according to Equation (7). In step 610, K_(e) and K_(o)are updated according to Equations (3) and (5), respectively. Accordingto an alternative exemplary embodiment, K_(e) and K_(o) can eachcomprise a predetermined value.

FIG. 7 is a flowchart illustrating steps for updating a filtercoefficient “b” of the second plurality of filter coefficients, inaccordance with an alternative exemplary embodiment of the presentinvention. In step 705, ΔΓ is updated according to Equation (10). Instep 710, K_(e) and K_(o) are updated according to Equations (3) and(5), respectively. According to an alternative exemplary embodiment,K_(e) and K_(o) can each comprise a predetermined value.

Any or all of the steps of a computer program as illustrated in FIGS.3A, 3B, and 4-7 for controlling at least one of gain and timing phasecan be embodied in any computer-readable medium for use by or inconnection with an instruction execution system, apparatus, or device,such as a computer-based system, processor-containing system, or othersystem that can fetch the instructions from the instruction executionsystem, apparatus, or device and execute the instructions. As usedherein, a “computer-readable medium” can be any means that can contain,store, communicate, or transport the program for use by or in connectionwith the instruction execution system, apparatus, or device. Thecomputer readable medium can be, for example but not limited to, anelectronic, magnetic, optical, electromagnetic, infrared, orsemiconductor system, apparatus, device, or. More specific examples (anon-exhaustive list) of the computer-readable medium can include thefollowing: a portable computer diskette, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), an optical fiber, and a portable compact discread-only memory (CDROM).

It will be appreciated by those of ordinary skill in the art that thepresent invention can be embodied in various specific forms withoutdeparting from the spirit or essential characteristics thereof. Thepresently disclosed embodiments are considered in all respects to beillustrative and not restrictive. The scope of the invention isindicated by the appended claims, rather than the foregoing description,and all changes that come within the meaning and range of equivalencethereof are intended to be embraced.

All United States patents and applications, foreign patents, andpublications discussed above are hereby incorporated herein by referencein their entireties.

1. An information communication system, comprising: a variable gain amplifier (VGA), wherein the VGA is responsive to an input signal of the information communication system; an analog-to-digital converter (ADC), wherein the ADC is responsive to an output of the VGA; a first filter, wherein tap weight coefficients of the first filter are updated according to a first least mean square (LMS) engine, wherein the first filter is responsive to an output of the ADC, and wherein at least two tap weight coefficients of the first filter are constrained; a second filter, wherein tap weight coefficients of the second filter are updated according to an adaptation engine, wherein the second filter is responsive to an output of the first filter, wherein a number of tap weight coefficients of the second filter comprises one of less than and equal to a number of the tap weight coefficients of the first filter, wherein the second filter comprises a three-tap filter, wherein tap weight coefficients of the three-tap filter comprise “a”, “1+b”, and “−a”, respectively, wherein a value of tap weight coefficient “a” of the second filter is updated to provide a timing phase of the second filter that is associated with a change in timing phase error introduced by the first filter, wherein the tap weight coefficient “a” is updated according to equation: a[n+1]=a[n]−α*Δθ, wherein a[n+1] comprises a value of the tap weight coefficient “a” for a next sampling time of the input signal, wherein a[n] comprises a value of the tap weight coefficient “a” for a current sampling time of the input signal, wherein α comprises a first gain constant, and wherein Δθ comprises a change in timing phase error associated with the first filter, wherein a value of tap weight coefficient “b” of the second filter is updated to provide a gain of the second filter that is associated with a change in gain error from the first filter, wherein the tap weight coefficient “b” is updated according to equation: b[n+1]=b[n]−β*ΔΓ, wherein b[n+1] comprises a value of the tap weight coefficient “b” for a next sampling time of the input signal, wherein b[n] comprises a value of the tap weight coefficient “b” for a current sampling time of the input signal, wherein β comprises a second gain constant, and wherein ΔΓ comprises a change in gain error from the first filter; a gain controller for controlling gain of the VGA, wherein the gain controller is in communication with the VGA and responsive to the output of the second filter, wherein the gain of the second filter is configured to cause the gain controller to modify a gain of the VGA to compensate for the change in gain error from the first filter; and a timing phase controller for controlling timing phase of the ADC, wherein the timing phase controller is in communication with the ADC and responsive to an output of the second filter, wherein the timing phase of the second filter is configured to cause the timing phase controller to modify a timing phase of the ADC to compensate for the change in timing phase error introduced by the first filter.
 2. The information communication system of claim 1, wherein the adaptation engine comprises one of a second LMS engine and a zero-forcing engine.
 3. The information communication system of claim 1, wherein the first filter comprises N tap weight coefficients, wherein N comprises at least four, wherein a third tap weight coefficient C₃ and a fourth tap weight coefficient C₄ of the first filter are constrained, and wherein Δθ is updated according to equation: ${{\Delta\theta} = \frac{\left( {{{- \Delta}\; C_{3}*K_{e}} - {\Delta\; C_{4}*K_{o}}} \right)}{K_{e}^{2} + K_{o}^{2}}},$ wherein ΔC₃ and ΔC₄ are updated according to equations: ΔC ₃ =μ*E[n]*X[n−3] and ΔC ₄ =μ*E[n]*X[n−4], respectively, wherein K_(e) and K_(o) are based on at least one of a tap weight coefficient and a predetermined value, wherein μ comprises a third gain constant, wherein E[n] comprises an error signal for a current sampling time of the input signal, wherein X[n−3] comprises a value of the input signal at a third previous sampling time of the input signal, and wherein X[n−4] comprises a value of the input signal at a fourth previous sampling time of the input signal.
 4. The information communication system of claim 3, wherein K_(e) and K_(o) are updated according to equations: ${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$ and ${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$ respectively, wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1” otherwise, wherein M is determined according to equation: M=TRUNCATE((N−1)/2), and wherein P is determined according to equation: P=TRUNCATE(((N−1)/2)−0.5).
 5. The information communication system of claim 3, wherein K_(e) and K_(o) each comprise a predetermined value.
 6. The information communication system of claim 3, wherein the error signal E[n] comprises a difference between an output of the first filter and an output of a reconstruction filter, wherein the reconstruction filter is responsive to an output of a sequence detector, and wherein the sequence detector is responsive to an output of the first filter.
 7. The information communication system of claim 1, wherein the first filter comprises N tap weight coefficients, wherein N comprises at least four, wherein a third tap weight coefficient C₃ and a fourth tap weight coefficient C₄ of the first filter are constrained, and wherein Δθ is updated according to equation: Δθ=(−ΔC ₃ *K _(e) −ΔC ₄ *K _(o)), wherein ΔC₃ and ΔC₄ are updated according to equations: ΔC ₃ =μ*E[n]*X[n−3] and ΔC ₄ =μ*E[n]*X[n−4], respectively, wherein K_(e) and K_(o) are based on at least one of a tap weight coefficient and a predetermined value, wherein μ comprises a third gain constant, wherein E[n] comprises an error signal for a current sampling time of the input signal, wherein X[n−3] comprises a value of the input signal at a third previous sampling time of the input signal, and wherein X[n−4] comprises a value of the input signal at a fourth previous sampling time of the input signal.
 8. The information communication system of claim 7, wherein K_(e) and K_(o) are updated according to equations: ${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$ and ${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$ respectively, and wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1” otherwise, wherein M is determined according to equation: M=TRUNCATE((N−1)/2), and wherein P is determined according to equation: P=TRUNCATE(((N−1)/2)−0.5).
 9. The information communication system of claim 7, wherein K_(e) and K_(o) each comprise a predetermined value.
 10. The information communication system of claim 7, wherein the error signal E[n] comprises a difference between an output of the first filter and an output of a reconstruction filter, wherein the reconstruction filter is in communication with an output of a sequence detector, and wherein the sequence detector is responsive to an output of the first filter.
 11. The information communication system of claim 1, wherein the first filter comprises N tap weight coefficients, wherein N comprises at least four, wherein a third tap weight coefficient C₃ and a fourth tap weight coefficient C₄ of the first filter are constrained, and wherein ΔΓ is updated according to equation: ${{\Delta\Gamma} = \frac{\left( {{{- \Delta}\; C_{3}*K_{o}} + {\Delta\; C_{4}*K_{e}}} \right)}{\sqrt{K_{e}^{2} + K_{o}^{2}}}},$ wherein ΔC₃ and ΔC₄ are updated according to equations: ΔC ₃ =μ*E[n]*X[n−3] and ΔC ₄ =μ*E[n]*X[n−4], respectively, wherein K_(e) and K_(o) are based on at least one of a tap weight coefficient and a predetermined value, wherein μ comprises a third gain constant, wherein E[n] comprises an error signal for a current sampling time of the input signal, wherein X[n−3] comprises a value of the input signal at a third previous sampling time of the input signal, and wherein X[n−4] comprises a value of the input signal at a fourth previous sampling time of the input signal.
 12. The information communication system of claim 11, wherein K_(e) and K_(o) are updated according to equations: ${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$ and ${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$ wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1” otherwise, wherein M is determined according to equation: M=TRUNCATE((N−1)/2), and wherein P is determined according to equation: P=TRUNCATE(((N−1)/2)−0.5).
 13. The information communication system of claim 11, wherein K_(e) and K_(o) each comprise a predetermined value.
 14. The information communication system of claim 11, wherein the error signal E[n] comprises a difference between an output of the first filter and an output of a reconstruction filter, wherein the reconstruction filter is responsive to an output of a sequence detector, and wherein the sequence detector is responsive to an output of the first filter.
 15. The information communication system of claim 1, wherein the first filter comprises N tap weight coefficients, wherein N comprises at least four, wherein a third tap weight coefficient C₃ and a fourth tap weight coefficient C₄ of the first filter are constrained, and wherein ΔΓ is updated according to equation: ΔΓ=(−ΔC ₃ *K _(o) +ΔC ₄ *K _(e)), wherein ΔC₃ and ΔC₄ are updated according to equations: ΔC ₃ =μ*E[n]*X[n−3] and ΔC ₄ =μ*E[n]*X[n−4], respectively, wherein K_(e) and K_(o) are based on at least one of a tap weight coefficient and a predetermined value, wherein μ comprises a third gain constant, wherein E[n] comprises an error signal for a current sampling time of the input signal, wherein X[n−3] comprises a value of the input signal at a third previous sampling time of the input signal, and wherein X[n−4] comprises a value of the input signal at a fourth previous sampling time of the input signal.
 16. The information communication system of claim 15, wherein K_(e) and K_(o) are updated according to equations: ${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$ and ${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$ respectively, and wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1” otherwise, wherein M is determined according to equation: M=TRUNCATE((N−1)/2), and wherein P is determined according to equation: P=TRUNCATE(((N−1)/2)−0.5).
 17. The information communication system of claim 15, wherein K_(e) and K_(o) each comprise a predetermined value.
 18. The information communication system of claim 15, wherein the error signal E[n] comprises a difference between an output of the first filter and an output of a reconstruction filter, wherein the reconstruction filter is responsive to an output of a sequence detector, and wherein the sequence detector is responsive to an output of the first filter.
 19. The information communication system of claim 1, comprising: a sequence detector, wherein the sequence detector is responsive to an output of the first filter.
 20. The information communication system of claim 19, comprising: a reconstruction filter, wherein the reconstruction filter is responsive to an output of the sequence detector.
 21. The information communication system of claim 20, comprising: an error generator in communication between an output of the second filter and inputs of the timing phase controller and the gain controller, wherein the error generator generates an error signal comprising a difference between an output of the first filter and an output of the reconstruction filter.
 22. The information communication system of claim 20, wherein the timing phase controller comprises an error generator, wherein the timing phase controller is responsive to an output of the first filter and an output of the reconstruction filter.
 23. The information communication system of claim 20, wherein the gain controller comprises an error generator, wherein the gain controller is responsive to an output of the first filter and an output of the reconstruction filter.
 24. An information communication system, comprising: a variable gain amplifier (VGA) means for amplifying an input signal of the information communication system; analog-to-digital converter (ADC) means for converting an output of the VGA means; first filter means for filtering an output of said ADC means, wherein tap weight coefficients of the first filter means are updated according to a first least mean square (LMS) engine means, wherein the first filter means is responsive to an output of the ADC means, and wherein at least two tap weight coefficients of the first filter means are constrained; second filter means for filtering an output of said first filter means, wherein tap weight coefficients of the second filter means are updated according to adaptation engine means for updating a tap weight coefficient, wherein the second filter means is responsive to an output of the first filter means, wherein a number of tap weight coefficients of the second filter means comprises one of less than and equal to a number of the tap weight coefficients of the first filter means, wherein the second filter means comprises a three-tap filter means, wherein tap weight coefficients of the three-tap filter means comprise “a”, “1+b”, and “−a”, respectively, wherein a value of tap weight coefficient “a” of the second filter means is updated to provide a timing phase of the second filter means that is associated with a change in timing phase error introduced by the first filter means, wherein the tap weight coefficient “a” is updated according to equation: a[n+1]=a[n]−α*Δθ, wherein a[n+1] comprises a value of the tap weight coefficient “a” for a next sampling time of the input signal, wherein a[n] comprises a value of the tap weight coefficient “a” for a current sampling time of the input signal, wherein α comprises a first gain constant, and wherein Δθ comprises a change in timing phase error associated with the first filter means, wherein a value of tap weight coefficient “b” of the second filter means is updated to provide a gain of the second filter means that is associated with a change in gain error from the first filter means, wherein the tap weight coefficient “b” is updated according to equation: b[n+1]=b[n]β*ΔΓ, wherein b[n+1] comprises a value of the tap weight coefficient “b” for a next sampling time of the input signal, wherein b[n] comprises a value of the tap weight coefficient “b” for a current sampling time of the input signal, wherein β comprises a second gain constant, and wherein ΔΓ comprises a change in gain error from the first filter means; gain controller means for controlling gain of the VGA means, wherein the gain controller means is in communication with the VGA means and responsive to the output of the second filter means, wherein the gain of the second filter means is configured to cause the gain controller means to modify a gain of the VGA means to compensate for the change in gain error from the first filter means; and timing phase controller means for controlling timing phase of the ADC means, wherein the timing phase controller means is in communication with the ADC means and responsive to an output of the second filter means, wherein the timing phase of the second filter means is configured to cause the timing phase controller means to modify a timing phase of the ADC means to compensate for the change in timing phase error introduced by the first filter means.
 25. The information communication system of claim 24, wherein the adaptation engine means comprises one of second LMS engine means and zero-forcing engine means for updating a tap weight coefficient.
 26. The information communication system of claim 24, wherein the first filter means comprises N tap weight coefficients, wherein N comprises at least four, wherein a third tap weight coefficient C₃ and a fourth tap weight coefficient C₄ of the first filter means are constrained, and wherein Δθ is updated according to equation: ${{\Delta\theta} = \frac{\left( {{{- \Delta}\; C_{3}*K_{e}} - {\Delta\; C_{4}*K_{o}}} \right)}{K_{e}^{2} + K_{o}^{2}}},$ wherein ΔC₃ and ΔC₄ are updated according to equations: ΔC ₃ =μ*E[n]*X[n−3] and ΔC ₄ =μ*E[n]*X[n−4], respectively, wherein K_(e) and K_(o) are based on at least one of a tap weight coefficient and a predetermined value, wherein μ comprises a third gain constant, wherein E[n] comprises an error signal for a current sampling time of the input signal, wherein X[n−3] comprises a value of the input signal at a third previous sampling time of the input signal, and wherein X[n−4] comprises a value of the input signal at a fourth previous sampling time of the input signal.
 27. The information communication system of claim 26, wherein K_(e) and K_(o) are updated according to equations: ${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$ and ${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$ respectively, wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1” otherwise, wherein M is determined according to equation: M=TRUNCATE((N−1)/2), and wherein P is determined according to equation: P=TRUNCATE(((N−1)/2)−0.5).
 28. The information communication system of claim 26, wherein K_(e) and K_(o) each comprise a predetermined value.
 29. The information communication system of claim 26, wherein the error signal E[n] comprises a difference between an output of the first filter means and an output of reconstruction filter means for reconstructing an information signal based on an output of a sequence detector means, wherein the sequence detector means is responsive to an output of the first filter means.
 30. The information communication system of claim 24, wherein the first filter means comprises N tap weight coefficients, wherein N comprises at least four, wherein a third tap weight coefficient C₃ and a fourth tap weight coefficient C₄ of the first filter means are constrained, and wherein Δθ is updated according to equation: Δθ=(−ΔC ₃ *K _(e) −ΔC ₄ *K _(o)), wherein ΔC₃ and ΔC₄ are updated according to equations: ΔC ₃ =μ*E[n]*X[n−3] and ΔC ₄ =μ*E[n]*X[n−4], respectively, wherein K_(e) and K_(o) are based on at least one of a tap weight coefficient and a predetermined value, wherein μ comprises a third gain constant, wherein E[n] comprises an error signal for a current sampling time of the input signal, wherein X[n−3] comprises a value of the input signal at a third previous sampling time of the input signal, and wherein X[n−4] comprises a value of the input signal at a fourth previous sampling time of the input signal.
 31. The information communication system of claim 30, wherein K_(e) and K_(o) are updated according to equations: ${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$ and ${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$ respectively, and wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1” otherwise, wherein M is determined according to equation: M=TRUNCATE((N−1)/2), and wherein P is determined according to equation: P=TRUNCATE(((N−1)/2)−0.5).
 32. The information communication system of claim 30, wherein K_(e) and K_(o) each comprise a predetermined value.
 33. The information communication system of claim 30, wherein the error signal E[n] comprises a difference between an output of the first filter means and an output of reconstruction filter means for reconstructing an information signal based on an output of a sequence detector means, wherein the sequence detector means is responsive to an output of the first filter means.
 34. The information communication system of claim 24, wherein the first filter means comprises N tap weight coefficients, wherein N comprises at least four, wherein a third tap weight coefficient C₃ and a fourth tap weight coefficient C₄ of the first filter means are constrained, and wherein ΔΓ is updated according to equation: ${{\Delta\Gamma} = \frac{\left( {{{- \Delta}\; C_{3}*K_{o}} + {\Delta\; C_{4}*K_{e}}} \right)}{\sqrt{K_{e}^{2} + K_{o}^{2}}}},$ wherein ΔC₃ and ΔC₄ are updated according to equations: ΔC ₃ =μ*E[n]*X[n−3] and ΔC ₄ =μ*E[n]*X[n−4], respectively, wherein K_(e) and K_(o) are based on at least one of a tap weight coefficient and a predetermined value, wherein μ comprises a third gain constant, wherein E[n] comprises an error signal for a current sampling time of the input signal, wherein X[n−3] comprises a value of the input signal at a third previous sampling time of the input signal, and wherein X[n−4] comprises a value of the input signal at a fourth previous sampling time of the input signal.
 35. The information communication system of claim 34, wherein K_(e) and K_(o) are updated according to equations: ${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$ and ${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$ respectively, wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1” otherwise, wherein M is determined according to equation: M=TRUNCATE((N−1)/2), and wherein P is determined according to equation: P=TRUNCATE(((N−1)/2)−0.5).
 36. The information communication system of claim 34, wherein K_(e) and K_(o) each comprise a predetermined value.
 37. The information communication system of claim 34, wherein the error signal E[n] comprises a difference between an output of the first filter means and an output of reconstruction filter means for reconstructing an information signal based on an output of a sequence detector means, wherein the sequence detector means is responsive to an output of the first filter means.
 38. The information communication system of claim 24, wherein the first filter means comprises N tap weight coefficients, wherein N comprises at least four, wherein a third tap weight coefficient C₃ and a fourth tap weight coefficient C₄ of the first filter means are constrained, and wherein ΔΓ is updated according to equation: ΔΓ=(−ΔC ₃ *K _(o) +ΔC ₄ *K _(e)), wherein ΔC₃ and ΔC₄ are updated according to equations: ΔC ₃ =μ*E[n]*X[n−3] and ΔC ₄ =μ*E[n]*X[n−4], respectively, wherein K_(e) and K_(o) are based on at least one of a tap weight coefficient and a predetermined value, wherein μ comprises a third gain constant, wherein E[n] comprises an error signal for a current sampling time of the input signal, wherein X[n−3] comprises a value of the input signal at a third previous sampling time of the input signal, and wherein X[n−4] comprises a value of the input signal at a fourth previous sampling time of the input signal.
 39. The information communication system of claim 38, wherein K_(e) and K_(o) are updated according to equations: ${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$ and ${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$ respectively, and wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1” otherwise, wherein M is determined according to equation: M=TRUNCATE((N−1)/2), and wherein P is determined according to equation: P=TRUNCATE(((N−1)/2)−0.5).
 40. The information communication system of claim 38, wherein K_(e) and K_(o) each comprise a predetermined value.
 41. The information communication system of claim 38, wherein the error signal E[n] comprises a difference between an output of the first filter means and an output of reconstruction filter means for reconstructing an information signal based on an output of a sequence detector means, and wherein the sequence detector means is responsive to an output of the first filter means.
 42. The information communication system of claim 24, further comprising sequence detector means for detecting an information sequence based on an output of the first filter means.
 43. The information communication system of claim 42, further comprising reconstruction filter means for reconstructing an information signal based on an output of the sequence detector means.
 44. The information communication system of claim 43, further comprising error generator means for generating an error signal, wherein said error generator means is in communication between an output of the second filter means and inputs of the timing phase controller means and the gain controller means, and wherein said error signal comprises a difference between an output of the first filter means and an output of the reconstruction filter means.
 45. The information communication system of claim 43, wherein the timing phase controller means comprises error generator means for generating an error signal based on an output of the first filter means and an output of the reconstruction filter means.
 46. The information communication system of claim 43, wherein the gain controller means comprises error generator means for generating an error signal, wherein the gain controller means is responsive to an output of the first filter means and an output of the reconstruction filter means.
 47. An information communication system, comprising: a variable gain amplifier (VGA), wherein the VGA is responsive to an input signal of the information communication system; an analog-to-digital converter (ADC), wherein the ADC is responsive to an output of the VGA; a first filter, wherein tap weight coefficients of the first filter are updated according to a first least mean square (LMS) engine, wherein the first filter is responsive to an output of the ADC, and wherein at least one tap weight coefficient of the first filter is constrained; a second filter, wherein the second filter is responsive to an output of the first filter, and wherein a number of tap weight coefficients of the second filter comprises one of less than and equal to a number of the tap weight coefficients of the first filter; a reconstruction filter that is responsive to the output of the first filter; and, at least one of: a gain controller for controlling gain of the VGA, wherein the gain controller is in communication with the VGA and responsive to the output of the second filter and an output of the reconstruction filter; and a timing phase controller for controlling timing phase of the ADC, wherein the timing phase controller is in communication with the ADC and responsive to an output of the second filter and an output of the reconstruction filter; and an error generator that signals the at least one of the gain controller and the timing phase controller based on the output of the second filter and an output of the reconstruction filter.
 48. The information communication system of claim 47, wherein tap weight coefficients of the second filter are updated according to an adaptation engine.
 49. The information communication system of claim 48, wherein the adaptation engine comprises one of a second LMS engine and a zero-forcing engine.
 50. The information communication system of claim 47, wherein the second filter comprises one of a two-tap filter and a three-tap filter.
 51. The information communication system of claim 50, wherein tap weight coefficients of the two-tap filter comprise “a” and “1+b”, respectively, and wherein tap weight coefficients of the three-tap filter comprise “a”, “1+b”, and “−a”, respectively.
 52. The information communication system of claim 51, wherein the tap weight coefficient “a” is updated according to equation: a[n+1]=a[n]−α*Δθ, wherein a[n+1] comprises a value of the tap weight coefficient “a” for a next sampling time of the input signal, wherein a[n] comprises a value of the tap weight coefficient “a” for a current sampling time of the input signal, wherein α comprises a first gain constant, and wherein Δθ comprises a change in timing phase error associated with the first filter.
 53. The information communication system of claim 52, wherein the first filter comprises N tap weight coefficients, wherein N comprises at least four, wherein a third tap weight coefficient C₃ and a fourth tap weight coefficient C₄ of the first filter are constrained, and wherein Δθ is updated according to equation: ${{\Delta\theta} = \frac{\left( {{{- \Delta}\; C_{3}*K_{e}} - {\Delta\; C_{4}*K_{o}}} \right)}{K_{e}^{2} + K_{o}^{2}}},$ wherein ΔC₃ and ΔC₄ are updated according to equations: ΔC ₃ =μ*E[n]*X[n−3] and ΔC ₄ =μ*E[n]*X[n−4], respectively, wherein K_(e) and K_(o) are based on at least one of a tap weight coefficient and a predetermined value, wherein μ comprises a second gain constant, wherein E[n] comprises an error signal for a current sampling time of the input signal, wherein X[n−3] comprises a value of the input signal at a third previous sampling time of the input signal, and wherein X[n−4] comprises a value of the input signal at a fourth previous sampling time of the input signal.
 54. The information communication system of claim 53, wherein K_(e) and K_(o) are updated according to equations: ${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$ and ${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$ respectively, wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1” otherwise, wherein M is determined according to equation: M=TRUNCATE((N−1)/2), and wherein P is determined according to equation: P=TRUNCATE(((N−1)/2)−0.5).
 55. The information communication system of claim 53, wherein K_(e) and K_(o) each comprise a predetermined value.
 56. The information communication system of claim 53, further comprising: a sequence detector, wherein the sequence detector is responsive to an output of the first filter; the reconstruction filter, wherein the reconstruction filter is responsive to an output of the sequence detector; and an error generator, wherein the error generator is responsive to the output of the first filter and an output of the reconstruction filter, and wherein the error generator generates the error signal E[n] comprising a difference between the output of the first filter and the output of the reconstruction filter.
 57. The information communication system of claim 52, wherein the first filter comprises N tap weight coefficients, wherein N comprises at least four, wherein a third tap weight coefficient C₃ and a fourth tap weight coefficient C₄ of the first filter are constrained, and wherein Δθ is updated according to equation: Δθ=(−ΔC ₃ *K _(e) −ΔC ₄ *K _(o)), wherein ΔC₃ and ΔC₄ are updated according to equations: ΔC ₃ =μ*E[n]*X[n−3] and ΔC ₄ =μ*E[n]*X[n−4], respectively, wherein K_(e) and K_(o) are based on at least one of a tap weight coefficient and a predetermined value, wherein μ comprises a second gain constant, wherein E[n] comprises an error signal for a current sampling time of the input signal, wherein X[n−3] comprises a value of the input signal at a third previous sampling time of the input signal, and wherein X[n−4] comprises a value of the input signal at a fourth previous sampling time of the input signal.
 58. The information communication system of claim 57, wherein K_(e) and K_(o) are updated according to equations: ${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$ and ${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$ respectively, and wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1” otherwise, wherein M is determined according to equation: M=TRUNCATE((N−1)/2), and wherein P is determined according to equation: P=TRUNCATE(((N−1)/2)−0.5).
 59. The information communication system of claim 57, wherein K_(e) and K_(o) each comprise a predetermined value.
 60. The information communication system of claim 57, further comprising: a sequence detector, wherein the sequence detector is responsive to an output of the first filter; the reconstruction filter, wherein the reconstruction filter is responsive to an output of the sequence detector; and an error generator, wherein the error generator is responsive to the output of the first filter and an output of the reconstruction filter, and wherein the error generator generates the error signal E[n] comprising a difference between the output of the first filter and the output of the reconstruction filter.
 61. The information communication system of claim 51, wherein the tap weight coefficient “b” is updated according to equation: b[n+1]=b[n]−β*ΔΓ, wherein b[n+1] comprises a value of the tap weight coefficient “b” for a next sampling time of the input signal, wherein b[n] comprises a value of the tap weight coefficient “b” for a current sampling time of the input signal, wherein β comprises a first gain constant, and wherein ΔΓ comprises a change in gain error from the first filter.
 62. The information communication system of claim 61, wherein the first filter comprises N tap weight coefficients, wherein N comprises at least four, wherein a third tap weight coefficient C₃ and a fourth tap weight coefficient C₄ of the first filter are constrained, and wherein ΔΓ is updated according to equation: ${{\Delta\Gamma} = \frac{\left( {{{- \Delta}\; C_{3}*K_{o}} + {\Delta\; C_{4}*K_{e}}} \right)}{\sqrt{K_{e}^{2} + K_{o}^{2}}}},$ wherein ΔC₃ and ΔC₄ are updated according to equations: ΔC ₃ =μ*E[n]*X[n−3] and ΔC ₄ =μ*E[n]*X[n−4], respectively, wherein K_(e) and K_(o) are based on at least one of a tap weight coefficient and a predetermined value, wherein μ comprises a second gain constant, wherein E[n] comprises an error signal for a current sampling time of the input signal, wherein X[n−3] comprises a value of the input signal at a third previous sampling time of the input signal, and wherein X[n−4] comprises a value of the input signal at a fourth previous sampling time of the input signal.
 63. The information communication system of claim 62, wherein K_(e) and K_(o) are updated according to equations: ${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$ and ${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$ respectively, wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1” otherwise, wherein M is determined according to equation: M=TRUNCATE((N−1)/2), and wherein P is determined according to equation: P=TRUNCATE(((N−1)/2)−0.5).
 64. The information communication system of claim 62, wherein K_(e) and K_(o) each comprise a predetermined value.
 65. The information communication system of claim 62, further comprising: a sequence detector, wherein the sequence detector is responsive to an output of the first filter; the reconstruction filter, wherein the reconstruction filter is responsive to an output of the sequence detector; and an error generator, wherein the error generator is responsive to the output of the first filter and an output of the reconstruction filter, wherein the error generator generates the error signal E[n] comprising a difference between the output of the first filter and the output of the reconstruction filter.
 66. The information communication system of claim 61, wherein the first filter comprises N tap weight coefficients, wherein N comprises at least four, wherein a third tap weight coefficient C₃ and a fourth tap weight coefficient C₄ of the first filter are constrained, and wherein ΔΓ is updated according to equation: ΔΓ=(−ΔC ₃ *K _(o) +ΔC ₄ *K _(e)), wherein ΔC₃ and ΔC₄ are updated according to equations: ΔC ₃ =μ*E[n]*X[n−3] and ΔC ₄ =μ*E[n]*X[n−4], respectively, wherein K_(e) and K_(o) are based on at least one of a tap weight coefficient and a predetermined value, wherein μ comprises a second gain constant, wherein E[n] comprises an error signal for a current sampling time of the input signal, wherein X[n−3] comprises a value of the input signal at a third previous sampling time of the input signal, and wherein X[n−4] comprises a value of the input signal at a fourth previous sampling time of the input signal.
 67. The information communication system of claim 66, wherein K_(e) and K_(o) are updated according to equations: ${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$ and ${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$ respectively, and wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1” otherwise, wherein M is determined according to equation: M=TRUNCATE((N−1)/2), and wherein P is determined according to equation: P=TRUNCATE(((N−1)/2)−0.5).
 68. The information communication system of claim 66, wherein K_(e) and K_(o) each comprise a predetermined value.
 69. The information communication system of claim 66, further comprising: a sequence detector, wherein the sequence detector is responsive to an output of the first filter; the reconstruction filter, wherein the reconstruction filter is responsive to an output of the sequence detector; and an error generator, wherein the error generator is responsive to the output of the first filter and an output of the reconstruction filter, wherein the error generator generates the error signal E[n] comprising a difference between the output of the first filter and the output of the reconstruction filter.
 70. The information communication system of claim 47, further comprising: a sequence detector, wherein the sequence detector is responsive to an output of the first filter; the reconstruction filter, wherein the reconstruction filter is responsive to an output of the sequence detector; and an error generator, wherein the error generator is responsive to an output of the reconstruction filter, and wherein the error generator is in communication with the second filter, the timing phase controller, and the gain controller.
 71. The information communication system of claim 70, wherein the timing phase controller is responsive to the output of the reconstruction filter.
 72. The information communication system of claim 70, wherein the gain controller is responsive to the output of the reconstruction filter.
 73. The information communication system of claim 47, wherein the first filter and the second filter each comprise a Finite Impulse Response filter.
 74. A disk drive comprising the information communication system of claim
 47. 75. The information communication system of claim 47, wherein at least the VGA, ADC, first filter, second filter, and at least one of the timing phase controller and gain controller are formed on a monolithic substrate.
 76. The information communication system of claim 47, wherein the information communication system is compliant with a standard selected from the group consisting of 802.11, 802.11a, 802.11b, 802.11g and 802.11i.
 77. The information communication system of claim 47 comprising said reconstruction filter, wherein said reconstruction filter is separate from said first filter and said second filter.
 78. The information communication system of claim 47 wherein said reconstruction filter is connected between said first filter and said at least one of said gain controller and said timing phase controller.
 79. The information communication system of claim 78 wherein said second filter is connected between said first filter and said at least one of said gain controller and said timing phase controller.
 80. The information communication system of claim 47 wherein said tap weight coefficients of said second filter are generated based on said output of said first filter.
 81. The information communication system of claim 80 wherein said tap weight coefficients of said first filter are generated based on said output of said first filter.
 82. The information communication system of claim 47 further comprising an adaptation engine that generates said tap weight coefficients of said second filter based on said output of said first filter and based on said output of said second filter.
 83. The information communication system of claim 47 wherein said output of said reconstruction filter is generated based on said output of said first filter.
 84. A method for controlling at least one of gain and timing phase of a communication system, comprising the steps of: a.) amplifying an input signal to generate an amplified signal; b.) converting the amplified signal into a digital signal to generate a converted signal; c.) filtering the converted signal to generate a first filtered signal in accordance with a first plurality of filter coefficients, wherein the first plurality of filter coefficients are updated according to a first least mean square (LMS) process, and wherein at least one filter coefficient of the first plurality of filter coefficients is constrained; d.) filtering the first filtered signal to generate a second filtered signal in accordance with a second plurality of filter coefficients, wherein a number of filter coefficients of the second plurality of filter coefficients comprises one of less than and equal to a number of the filter coefficients of the first plurality of filter coefficients; e.) generating a reconstruction filter output in response to the first filtered signal; f.) controlling at least one of a gain of step (a.) and a timing phase of step (b.) in response to the second filtered signal and the reconstruction filter output; and g.) controlling the at least one of the gain of step (a.) via a gain controller and the timing phase of step (b.) based on a signal that is generated by an error generator and based on the second filtered signal and the reconstruction filter output.
 85. The method of claim 84, wherein the second plurality of filter coefficients are updated according to an adaptation process.
 86. The method of claim 85, wherein the adaptation process comprises one of a second LMS process and a zero-forcing process.
 87. The method of claim 84, wherein the second plurality of filter coefficients comprises one of two and three filter coefficients.
 88. The method of claim 87, wherein the two filter coefficients of the second plurality of filter coefficients comprise “a” and “1+b”, respectively, and wherein the three filter coefficients of the second plurality of filter coefficients comprise “a”, “1+b”, and “−a”, respectively.
 89. The method of claim 88, further comprising the step of: g.) updating the filter coefficient “a” according to equation: a[n+1]=a[n]−α*Δθ, wherein a[n+1] comprises a value of the tap weight coefficient “a” for a next sampling time of the input signal, wherein a[n] comprises a value of the tap weight coefficient “a” for a current sampling time of the input signal, wherein α comprises a first gain constant, and wherein Δθ comprises a change in timing phase error associated with step (c.).
 90. The method of claim 89, wherein the first plurality of filter coefficients comprises N filter coefficients, wherein N comprises at least four, wherein a third filter coefficient C₃ and a fourth filter coefficient C₄ of the first plurality of filter coefficients are constrained, and wherein the method further comprises the step of: h.) updating Δθ according to equation: ${{\Delta\theta} = \frac{\left( {{{- \Delta}\; C_{3}*K_{e}} - {\Delta\; C_{4}*K_{o}}} \right)}{K_{e}^{2} + K_{o}^{2}}},$ wherein ΔC₃ and ΔC₄ are updated according to equations: ΔC ₃ =μ*E[n]*X[n−3] and ΔC ₄ =μ*E[n]*X[n−4], respectively, wherein K_(e) and K_(o) are based on at least one of a tap weight coefficient and a predetermined value, wherein μ comprises a second gain constant, wherein E[n] comprises an error signal for a current sampling time of the input signal, wherein X[n−3] comprises a value of the input signal at a third previous sampling time of the input signal, and wherein X[n−4] comprises a value of the input signal at a fourth previous sampling time of the input signal.
 91. The method of claim 90, further comprising the step of: i.) updating K_(e) and K_(o) according to equations: ${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$  and ${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$  respectively, wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1” otherwise, wherein M is determined according to equation: M=TRUNCATE((N−1)/2), and wherein P is determined according to equation: P=TRUNCATE(((N−1)/2)−0.5).
 92. The method of claim 90, wherein K_(e) and K_(o) each comprise a predetermined value.
 93. The method of claim 90, further comprising the steps of: i.) detecting an information sequence in the first filtered signal; j.) reconstructing an information signal from the detected information sequence; and k.) generating the error signal E[n] comprising a difference between the first filtered signal and the reconstructed information signal.
 94. The method of claim 89, wherein the first plurality of filter coefficients comprises N filter coefficients, wherein N comprises at least four, wherein a third filter coefficient C₃ and a fourth filter coefficient C₄ of the first plurality of filter coefficients are constrained, and wherein the method further comprises the step of: h.) updating Δθ according to equation: Δθ=(−ΔC ₃ *K _(e) −ΔC ₄ *K _(o)), wherein ΔC₃ and ΔC₄ are updated according to equations: ΔC ₃ =μ*E[n]*X[n−3] and ΔC ₄ =μ*E[n]*X[n−4], respectively, wherein K_(e) and K_(o) are based on at least one of a tap weight coefficient and a predetermined value, wherein μ comprises a second gain constant, wherein E[n] comprises an error signal for a current sampling time of the input signal, wherein X[n−3] comprises a value of the input signal at a third previous sampling time of the input signal, and wherein X[n−4] comprises a value of the input signal at a fourth previous sampling time of the input signal.
 95. The method of claim 94, further comprising the step of: i.) updating K_(e) and K_(o) according to equations: ${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$  and ${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$  respectively, and wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1” otherwise, wherein M is determined according to equation: M=TRUNCATE((N−1)/2), and wherein P is determined according to equation: P=TRUNCATE(((N−1)/2)−0.5).
 96. The method of claim 94, wherein K_(e) and K_(o) each comprise a predetermined value.
 97. The method of claim 94, further comprising the steps of: i.) detecting an information sequence in the first filtered signal; j.) reconstructing an information signal from the detected information sequence; and k.) generating the error signal E[n] comprising a difference between the first filtered signal and the reconstructed information signal.
 98. The method of claim 88, further comprising the step of: g.) updating the tap weight coefficient “b” according to equation: b[n+1]=b[n]−β*ΔΓ, wherein b[n+1] comprises a value of the tap weight coefficient “b” for a next sampling time of the input signal, wherein b[n] comprises a value of the tap weight coefficient “b” for a current sampling time of the input signal, wherein β comprises a first gain constant, and wherein ΔΓ comprises a change in gain error from step (c.).
 99. The method of claim 98, wherein the first plurality of filter coefficients comprises N filter coefficients, wherein N comprises at least four, wherein a third filter coefficient C₃ and a fourth filter coefficient C₄ of the first plurality of filter coefficients are constrained, and wherein the method further comprises the step of: h.) updating ΔΓ according to equation: ${{\Delta\Gamma} = \frac{\left( {{{- \Delta}\; C_{3}*K_{o}} + {\Delta\; C_{4}*K_{e}}} \right)}{\sqrt{K_{e}^{2} + K_{o}^{2}}}},$ wherein ΔC₃ and ΔC₄ are updated according to equations: ΔC ₃ =μ*E[n]*X[n−3] and ΔC ₄ =μ*E[n]*X[n−4], respectively, wherein K_(e) and K_(o) are based on at least one of a tap weight coefficient and a predetermined value, wherein μ comprises a second gain constant, wherein E[n] comprises an error signal for a current sampling time of the input signal, wherein X[n−3] comprises a value of the input signal at a third previous sampling time of the input signal, and wherein X[n−4] comprises a value of the input signal at a fourth previous sampling time of the input signal.
 100. The method of claim 99, further comprising the step of: i.) updating K_(e) and K_(o) according to equations: ${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$  and ${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$  respectively, wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1” otherwise, wherein M is determined according to equation: M=TRUNCATE((N−1)/2), and wherein P is determined according to equation: P=TRUNCATE(((N−1)/2)−0.5).
 101. The method of claim 99, wherein K_(e) and K_(o) each comprise a predetermined value.
 102. The method of claim 99, further comprising the steps of: i.) detecting an information sequence in the first filtered signal; j.) reconstructing an information signal from the detected information sequence; and k.) generating the error signal E[n] comprising a difference between the first filtered signal and the reconstructed information signal.
 103. The method of claim 98, wherein the first plurality of filter coefficients comprises N filter coefficients, wherein N comprises at least four, wherein a third filter coefficient C₃ and a fourth filter coefficient C₄ of the first plurality of filter coefficients are constrained, and wherein the method further comprises the step of: h.) updating ΔΓ according to equation: ΔΓ=(−ΔC ₃ *K _(o) +ΔC ₄ *K _(e)), wherein ΔC₃ and ΔC₄ are updated according to equations: ΔC ₃ =μ*E[n]*X[n−3] and ΔC ₄ =μ*E[n]*X[n−4], respectively, wherein K_(e) and K_(o) are based on at least one of a tap weight coefficient and a predetermined value, wherein μ comprises a second gain constant, wherein E[n] comprises an error signal for a current sampling time of the input signal, wherein X[n−3] comprises a value of the input signal at a third previous sampling time of the input signal, and wherein X[n−4] comprises a value of the input signal at a fourth previous sampling time of the input signal.
 104. The method of claim 103, further comprising the step of: i.) updating K_(e) and K_(o) according to equations: ${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$  and ${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$  respectively, and wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1” otherwise, wherein M is determined according to equation: M=TRUNCATE((N−1)/2), and wherein P is determined according to equation: P=TRUNCATE(((N−1)/2)−0.5).
 105. The method of claim 103, wherein K_(e) and K_(o) each comprise a predetermined value.
 106. The method of claim 103, further comprising the steps of: i.) detecting an information sequence in the first filtered signal; j.) reconstructing an information signal from the detected information sequence; and k.) generating the error signal E[n] comprising a difference between the first filtered signal and the reconstructed information signal.
 107. The method of claim 84, further comprising the steps of: g.) detecting an information sequence in the first filtered signal; h.) reconstructing an information signal from the detected information sequence; and i.) generating an error signal, wherein the error signal is associated with the reconstructed information signal.
 108. The method of claim 84, wherein the method is compliant with a standard selected from the group consisting of 802.11, 802.11a, 802.11b, 802.11g and 802.11i.
 109. A method for controlling at least one of gain and timing phase of a communication system, comprising the steps of: a.) amplifying an input signal to generate an amplified signal; b.) converting the amplified signal into a digital signal to generate a converted signal; c.) filtering the converted signal to generate a first filtered signal in accordance with a first plurality of filter coefficients, wherein the first plurality of filter coefficients are updated according to a first least mean square (LMS) process, and wherein at least one filter coefficient of the first plurality of filter coefficients is constrained; d.) filtering the first filtered signal to generate a second filtered signal in accordance with a second plurality of filter coefficients, wherein a number of filter coefficients of the second plurality of filter coefficients comprises one of less than and equal to a number of the filter coefficients of the first plurality of filter coefficients; and e.) controlling at least one of a gain of step (a.) via a gain controller and a timing phase of step (b.) in response to the second filtered signal, wherein at least two filter coefficients of the first plurality of filter coefficients are constrained, and wherein the method further comprises the steps of: f.) updating a value of at least one filter coefficient of the second plurality of filter coefficients to provide a gain of step (d.) that is associated with a change in gain error from step (c.); and g.) modifying the gain of step (a.) based upon the gain of step (d.), to compensate for the change in gain error from step (c.).
 110. A method for controlling at least one of gain and timing phase of a communication system, comprising the steps of: a.) amplifying an input signal to generate an amplified signal; b.) converting the amplified signal into a digital signal to generate a converted signal; c.) filtering the converted signal to generate a first filtered signal in accordance with a first plurality of filter coefficients, wherein the first plurality of filter coefficients are updated according to a first least mean square (LMS) process, and wherein at least one filter coefficient of the first plurality of filter coefficients is constrained; d.) filtering the first filtered signal to generate a second filtered signal in accordance with a second plurality of filter coefficients, wherein a number of filter coefficients of the second plurality of filter coefficients comprises one of less than and equal to a number of the filter coefficients of the first plurality of filter coefficients; and e.) controlling at least one of a gain of step (a.) via a gain controller and a timing phase of step (b.) in response to the second filtered signal, wherein at least two filter coefficients of the first plurality of filter coefficients are constrained, and where the method further comprises the steps of: f.) updating a value of at least one filter coefficient of the second plurality of filter coefficients to provide a timing phase of step (d.) that is associated with a change in timing phase error introduced by step (c.); and g.) modifying a timing phase of step (b.) based upon the timing phase of step (d.), to compensate for the change in timing phase error introduced by step (c.).
 111. An information communication system, comprising: a variable gain amplifier (VGA), wherein the VGA is responsive to an input signal of the information communication system; an analog-to-digital converter (ADC), wherein the ADC is responsive to an output of the VGA; a first filter, wherein tap weight coefficients of the first filter are updated according to a first least mean square (LMS) engine, wherein the first filter is responsive to an output of the ADC, and wherein at least one tap weight coefficient of the first filter is constrained; a second filter, wherein the second filter is responsive to an output of the first filter, and wherein a number of tap weight coefficients of the second filter comprises one of less than and equal to a number of the tap weight coefficients of the first filter; and, at least one of: a gain controller for controlling gain of the VGA, wherein the gain controller is in communication with the VGA and responsive to the output of the second filter; and a timing phase controller for controlling timing phase of the ADC, wherein the timing phase controller is in communication with the ADC and responsive to an output of the second filter, wherein at least two tap weight coefficients of the first filter are constrained, wherein a value of at least one tap weight coefficient of the second filter is updated to provide a gain of the second filter that is associated with a change in gain error from the first filter, and wherein the gain of the second filter is configured to cause the gain controller to modify a gain of the VGA to compensate for the change in gain error from the first filter.
 112. An information communication system, comprising: a variable gain amplifier (VGA), wherein the VGA is responsive to an input signal of the information communication system; an analog-to-digital converter (ADC), wherein the ADC is responsive to an output of the VGA; a first filter, wherein tap weight coefficients of the first filter are updated according to a first least mean square (LMS) engine, wherein the first filter is responsive to an output of the ADC, and wherein at least one tap weight coefficient of the first filter is constrained; a second filter, wherein the second filter is responsive to an output of the first filter, and wherein a number of tap weight coefficients of the second filter comprises one of less than and equal to a number of the tap weight coefficients of the first filter; and, at least one of: a gain controller for controlling gain of the VGA, wherein the gain controller is in communication with the VGA and responsive to the output of the second filter; and a timing phase controller for controlling timing phase of the ADC, wherein the timing phase controller is in communication with the ADC and responsive to an output of the second filter, wherein at least two tap weight coefficients of the first filter are constrained, wherein a value of at least one tap weight coefficient of the second filter is updated to provide a timing phase of the second filter that is associated with a change in timing phase error introduced by the first filter, and wherein the timing phase of the second filter is configured to cause the timing phase controller to modify a timing phase of the ADC to compensate for the change in timing phase error introduced by the first filter.
 113. An information communication system, comprising: means for amplifying an input signal received by the information communication system to generate an amplified signal; means for converting the amplified signal into a digital signal to generate a converted signal; first means for filtering the converted signal to generate a first filtered signal, wherein tap weight coefficients of the first means for filtering are updated according to a first least mean square (LMS) adaptation means, wherein at least one tap weight coefficient of the first means for filtering is constrained; second means for filtering the first filtered signal to generate a second filtered signal, wherein a number of tap weight coefficients of the second means for filtering comprises one of less than and equal to a number of the tap weight coefficients of the first means for filtering; reconstruction means for generating a reconstruction filter output in response to the first filtered signal; means for controlling at least one of a gain of the means for amplifying; and a timing phase of the means for converting in response to the second filtered signal and the reconstruction filter output; and error generating means for signaling the means for controlling based on the second filtered signal and the reconstruction filter output.
 114. The information communication system of claim 113, wherein tap weight coefficients of the second means for filtering are updated according to adaptation means for updating a tap weight coefficient.
 115. The information communication system of claim 114, wherein the adaptation means comprises one of second LMS adaptation means and zero-forcing adaptation means for updating a tap weight coefficient.
 116. The information communication system of claim 113, wherein at least two tap weight coefficients of the first means for filtering are constrained, and wherein the information communication system further comprises: means for updating a value of at least one tap weight coefficient of the second means for filtering to provide a gain of the second means for filtering that is associated with a change in gain error from the first means for filtering; and means for modifying a gain of the means for amplifying based upon the gain of the second means for filtering, to compensate for the change in gain error from the first means for filtering.
 117. The information communication system of claim 113, wherein at least two tap weight coefficients of the first means for filtering are constrained, and where the information communication system further comprises: means for updating a value of at least one tap weight coefficient of the second means for filtering to provide a timing phase of the second means for filtering that is associated with a change in timing phase error introduced by the first means for filtering; and means for modifying a timing phase of the means for converting based upon the timing phase of the second means for filtering, to compensate for the change in timing phase error introduced by the first means for filtering.
 118. The information communication system of claim 113, wherein the second means for filtering comprises one of two-tap filter means and three-tap filter means for filtering said first filtered signal.
 119. The information communication system of claim 118, wherein tap weight coefficients of the two-tap filter means comprise “a” and “1+b”, respectively, and wherein tap weight coefficients of the three-tap filter means comprise “a”, “1+b”, and “−a”, respectively.
 120. The information communication system of claim 119, further comprising: means for updating the tap weight coefficient “a” according to equation: a[n+1]=a[n]−α*Δθ, wherein a[n+1] comprises a value of the tap weight coefficient “a” for a next sampling time of the input signal, wherein a[n] comprises a value of the tap weight coefficient “a” for a current sampling time of the input signal, wherein α comprises a first gain constant, and wherein Δθ comprises a change in timing phase error associated with the first means for filtering.
 121. The information communication system of claim 120, wherein the first means for filtering comprises N tap weight coefficients, wherein N comprises at least four, wherein a third tap weight coefficient C₃ and a fourth tap weight coefficient C₄ of the first means for filtering are constrained, and wherein the means for updating the tap weight coefficient comprises: means for updating Δθ according to equation: ${{\Delta\theta} = \frac{\left( {{{- \Delta}\; C_{3}*K_{e}} - {\Delta\; C_{4}*K_{o}}} \right)}{K_{e}^{2} + K_{o}^{2}}},$ wherein ΔC₃ and ΔC₄ are updated according to equations: ΔC ₃ =μ*E[n]*X[n−3] and ΔC ₄ =μ*E[n]*X[n−4], respectively, wherein K_(e) and K_(o) are based on at least one of a tap weight coefficient and a predetermined value, wherein μ comprises a second gain constant, wherein E[n] comprises an error signal for a current sampling time of the input signal, wherein X[n−3] comprises a value of the input signal at a third previous sampling time of the input signal, and wherein X[n−4] comprises a value of the input signal at a fourth previous sampling time of the input signal.
 122. The information communication system of claim 121, wherein the means for updating the tap weight coefficient comprises: means for updating K_(e) and K_(o) according to equations: ${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$  and ${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$  respectively, wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1” otherwise, wherein M is determined according to equation: M=TRUNCATE((N−1)/2), and wherein P is determined according to equation: P=TRUNCATE(((N−1)/2)−0.5).
 123. The information communication system of claim 121, wherein K_(e) and K_(o) each comprise a predetermined value.
 124. The information communication system of claim 121, comprising: means for detecting an information sequence in the first filtered signal, wherein the means for detecting is responsive to an output of the first means for filtering; means for reconstructing an information signal from the information sequence, wherein the means for reconstructing is responsive to an output of the means for detecting; and means for generating an error signal, wherein the means for generating an error signal is responsive to the output of the first means for filtering and an output of the means for reconstructing, and wherein the means for generating an error signal generates the error signal E[n] comprising a difference between the output of the first means for filtering and the output of the means for reconstructing.
 125. The information communication system of claim 120, wherein the first means for filtering comprises N tap weight coefficients, wherein N comprises at least four, wherein a third tap weight coefficient C₃ and a fourth tap weight coefficient C₄ of the first means for filtering are constrained, and wherein the means for updating the tap weight coefficient comprises: means for updating Δθ according to equation: Δθ=(−ΔC ₃ *K _(e) −ΔC ₄ *K _(o)), wherein ΔC₃ and ΔC₄ are updated according to equations: ΔC ₃ =μ*E[n]*X[n−3] and ΔC ₄ =μ*E[n]*X[n−4], respectively, wherein K_(e) and K_(o) are based on at least one of a tap weight coefficient and a predetermined value, wherein μ comprises a second gain constant, wherein E[n] comprises an error signal for a current sampling time of the input signal, wherein X[n−3] comprises a value of the input signal at a third previous sampling time of the input signal, and wherein X[n−4] comprises a value of the input signal at a fourth previous sampling time of the input signal.
 126. The information communication system of claim 125, wherein the means for updating the tap weight coefficient comprises: means for updating K_(e) and K_(o) according to equations: ${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$  and ${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$  respectively, and wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1” otherwise, wherein M is determined according to equation: M=TRUNCATE((N−1)/2), and wherein P is determined according to equation: P=TRUNCATE(((N−1)/2)−0.5).
 127. The information communication system of claim 125, wherein K_(e) and K_(o) each comprise a predetermined value.
 128. The information communication system of claim 125, comprising: means for detecting an information sequence in the first filtered signal, wherein the means for detecting is responsive to an output of the first means for filtering; means for reconstructing an information signal from the information sequence, wherein the means for reconstructing is responsive to an output of the means for detecting; and means for generating an error signal, wherein the means for generating an error signal is responsive to the output of the first means for filtering and an output of the means for reconstructing, and wherein the means for generating an error signal generates the error signal E[n] comprising a difference between the output of the first means for filtering and the output of the means for reconstructing.
 129. The information communication system of claim 119, further comprising: means for updating the tap weight coefficient “b” according to equation: b[n+1]=b[n]−β*ΔΓ, wherein b[n+1] comprises a value of the tap weight coefficient “b” for a next sampling time of the input signal, wherein b[n] comprises a value of the tap weight coefficient “b” for a current sampling time of the input signal, wherein β comprises a first gain constant, and wherein ΔΓ comprises a change in gain error from the first means for filtering.
 130. The information communication system of claim 129, wherein the first means for filtering comprises N tap weight coefficients, wherein N comprises at least four, wherein a third tap weight coefficient C₃ and a fourth tap weight coefficient C₄ of the first means for filtering are constrained, and wherein the means for updating the tap weight coefficient comprises: means for updating ΔΓ according to equation: ${{\Delta\Gamma} = \frac{\left( {{{- \Delta}\; C_{3}*K_{o}} + {\Delta\; C_{4}*K_{e}}} \right)}{\sqrt{K_{e}^{2} + K_{o}^{2}}}},$ wherein ΔC₃ and ΔC₄ are updated according to equations: ΔC ₃ =μ*E[n]*X[n−3] and ΔC ₄ =μ*E[n]*X[n−4], respectively, wherein K_(e) and K_(o) are based on at least one of a tap weight coefficient and a predetermined value, wherein μ comprises a second gain constant, wherein E[n] comprises an error signal for a current sampling time of the input signal, wherein X[n−3] comprises a value of the input signal at a third previous sampling time of the input signal, and wherein X[n−4] comprises a value of the input signal at a fourth previous sampling time of the input signal.
 131. The information communication system of claim 130, wherein the means for updating the tap weight coefficient comprises: means for updating K_(e) and K_(o) according to equations: ${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$  and ${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$  respectively, wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1” otherwise, wherein M is determined according to equation: M=TRUNCATE((N−1)/2), and wherein P is determined according to equation: P=TRUNCATE(((N−1)/2)−0.5).
 132. The information communication system of claim 130, wherein K_(e) and K_(o) each comprise a predetermined value.
 133. The information communication system of claim 130, comprising: means for detecting an information sequence in the first filtered signal, wherein the means for detecting is responsive to an output of the first means for filtering; means for reconstructing an information signal from the information sequence, wherein the means for reconstructing is responsive to an output of the means for detecting; and means for generating an error signal, wherein the means for generating an error signal is responsive to the output of the first means for filtering and an output of the means for reconstructing, and wherein the means for generating an error signal generates the error signal E[n] comprising a difference between the output of the first means for filtering and the output of the means for reconstructing.
 134. The information communication system of claim 129, wherein the first means for filtering comprises N tap weight coefficients, wherein N comprises at least four, wherein a third tap weight coefficient C₃ and a fourth tap weight coefficient C₄ of the first means for filtering are constrained, and wherein the means for updating the tap weight coefficient comprises: means for updating ΔΓ according to equation: ΔΓ=(−ΔC ₃ *K _(o) +ΔC ₄ *K _(e)), wherein ΔC₃ and ΔC₄ are updated according to equations: ΔC ₃ =μ*E[n]*X[n−3] and ΔC ₄ =μ*E[n]*X[n−4], respectively, wherein K_(e) and K_(o) are based on at least one of a tap weight coefficient and a predetermined value, wherein μ comprises a second gain constant, wherein E[n] comprises an error signal for a current sampling time of the input signal, wherein X[n−3] comprises a value of the input signal at a third previous sampling time of the input signal, and wherein X[n−4] comprises a value of the input signal at a fourth previous sampling time of the input signal.
 135. The information communication system of claim 134, wherein the means for updating the tap weight coefficient comprises: means for updating K_(e) and K_(o) according to equations: ${K_{e} = {\sum\limits_{n = 0}^{M}\;{\gamma\; C_{2n}}}},$  and ${K_{o} = {\sum\limits_{n = 0}^{P}\;{\gamma\; C_{{2n} + 1}}}},$  respectively, and wherein γ comprises a “+1” when ((2*n) modulo 4)=0 and comprises a “−1” otherwise, wherein M is determined according to equation: M=TRUNCATE((N−1)/2), and wherein P is determined according to equation: P=TRUNCATE(((N−1)/2)−0.5).
 136. The information communication system of claim 134, wherein K_(e) and K_(o) each comprise a predetermined value.
 137. The information communication system of claim 134, comprising: means for detecting an information sequence in the first filtered signal, wherein the means for detecting is responsive to an output of the first means for filtering; means for reconstructing an information signal from the information sequence, wherein the means for reconstructing is responsive to an output of the means for detecting; and means for generating an error signal, wherein the means for generating an error signal is responsive to the output of the first means for filtering and an output of the means for reconstructing, and wherein the means for generating an error signal generates the error signal E[n] comprising a difference between the output of the first means for filtering and the output of the means for reconstructing.
 138. The information communication system of claim 113, comprising: means for detecting an information sequence in the first filtered signal, wherein the means for detecting is responsive to an output of the first means for filtering; means for reconstructing an information signal from the information sequence, wherein the means for reconstructing is responsive to an output of the means for detecting; and means for generating an error signal, wherein the means for generating an error signal is responsive to an output of the means for reconstructing, and wherein the means for generating an error signal is in communication between an output of the second means for filtering and inputs of the means for controlling the gain and the means for controlling the timing phase.
 139. The information communication system of claim 113, wherein the first means for filtering and the second means for filtering each comprise a Finite Impulse Response filter means.
 140. A disk drive comprising the information communication system of claim
 113. 141. The information communication system of claim 113, wherein at least the means for amplifying, the means for converting, the first means for filtering, the second means for filtering, and at least one of the means for controlling a gain of the means for amplifying and the means for controlling a timing phase of the means for converting is formed on a monolithic substrate.
 142. The information communication system of claim 113, wherein the information communication system is compliant with a standard selected from the group consisting of 802.11, 802.11a, 802.11b, 802.11g and 802.11i.
 143. An information communication system, comprising: a variable gain amplifier (VGA), wherein the VGA is responsive to an input signal of the information communication system; an analog-to-digital converter (ADC), wherein the ADC is responsive to an output of the VGA; a first filter, wherein tap weight coefficients of the first filter are updated according to a first least mean square (LMS) engine, wherein the first filter is responsive to an output of the ADC, and wherein at least one tap weight coefficient of the first filter is constrained; a second filter, wherein the second filter is responsive to an output of the first filter, and wherein a number of tap weight coefficients of the second filter comprises one of less than and equal to a number of the tap weight coefficients of the first filter; at least one of: a gain controller for controlling gain of the VGA, wherein the gain controller is in communication with the VGA and responsive to an output of the second filter; and a timing phase controller for controlling timing phase of the ADC, wherein the timing phase controller is in communication with the ADC and responsive to an output of the second filter; and a first error generator that is responsive to said output of the second filter and an output of a reconstruction filter that is connected between said first filter and said first error generator, wherein said at least one of said gain controller and said timing phase controller is responsive to said first error generator.
 144. The information communication system of claim 130 further comprising a second error generator that is responsive to said output of said first filter, wherein said tap weight coefficients of said first filter are generated based on an output of said second error generator.
 145. The information communication system of claim 144 wherein said tap weight coefficients of said first filter are generated based on an output of the reconstruction filter.
 146. An information communication system, comprising: means for amplifying an input signal received by the information communication system to generate an amplified signal; means for converting the amplified signal into a digital signal to generate a converted signal; first means for filtering the converted signal to generate a first filtered signal, wherein tap weight coefficients of the first means for filtering are updated according to a first least mean square (LMS) adaptation means, wherein at least one tap weight coefficient of the first means for filtering is constrained; second means for filtering the first filtered signal to generate a second filtered signal, wherein a number of tap weight coefficients of the second means for filtering comprises one of less than and equal to a number of the tap weight coefficients of the first means for filtering; at least one of: means for controlling a gain of the means for amplifying in response to the second filtered signal; means for controlling a timing phase of the means for converting in response to the second filtered signal; and error generating means for generating an output signal in response to said output of the second filter and an output of a reconstruction filter that is connected between said first means for filtering and said error generating means, wherein said at least one of means for controlling a gain and means for controlling a timing phase is responsive to said error generating means.
 147. A computer readable medium that stores a computer program, said computer program when executed by a processor, causes the processor to control at least one of gain and timing phase of a communication system by performing the steps of: a.) filtering an input signal to generate a first filtered signal in accordance with a first plurality of filter coefficients; b.) updating the first plurality of filter coefficients according to a first least mean square (LMS) process; c.) constraining at least one filter coefficient of the first plurality of filter coefficients; d.) filtering the first filtered signal to generate a second filtered signal in accordance with a second plurality of filter coefficients, wherein a number of filter coefficients of the second plurality of filter coefficients comprises one of less than and equal to a number of the filter coefficients of the first plurality of filter coefficients; e.) generating a reconstruction filter output in response to the first filtered signal; and f.) generating an error generator output in response to the second filtered signal and said reconstruction filter output; g.) outputting at least one of a gain control signal and a timing phase control signal in response to the error generator output from step (f.). 